Semantic segmentation on resource-constrained hardware remains a key challenge in deep learning, particularly for deployment on edge devices and embedded systems. In this study, we propose FireSegUNet, a lightweight and computationally efficient deep-learning architecture tailored for such environments. The model integrates an optimized inverted bottleneck layer for feature extraction within an encoder–decoder framework, reducing computational complexity by up to 51%. It also improves segmentation accuracy through an efficient squeeze-and-excitation block, while reducing inference time by up to 7.3 × and energy consumption by up to 4.6 × compared to conventional attention mechanisms. Extensive evaluation on diverse fire segmentation datasets demonstrates that FireSegUNet achieves competitive segmentation accuracy while reducing the number of parameters and storage requirements by up to 81%. Additionally, we provide a detailed analysis of the relationship between model complexity metrics and actual inference time, memory usage, and energy consumption. This comprehensive evaluation confirms that FireSegUNet delivers better performance on edge devices and generalizes well to unseen datasets. These findings position FireSegUNet as a practical solution for efficient image segmentation in resource-constrained environments. Although primarily validated on fire segmentation, the modular design of FireSegUNet makes it adaptable to other computer vision tasks. The source code of FireSegUNet will be publicly available at https://github.com/Realistic3D-MIUN/FireSegUNet .

Text-driven 3D scene editing has attracted considerable interest due to its convenience and user-friendliness. However, methods that rely on implicit 3D representations, such as Neural Radiance Fields (NeRF), while effective in rendering complex scenes, are hindered by slow processing speeds and limited control over specific regions of the scene. Moreover, existing approaches, including Instruct-NeRF2NeRF and GaussianEditor, which utilize multi-view editing strategies, frequently produce inconsistent results across different views when executing text instructions. This inconsistency can adversely affect the overall performance of the model, complicating the task of balancing the consistency of editing results with editing efficiency. To address these challenges, we propose a novel method termed Single-View to 3D Object Editing via Gaussian Splatting (SVGS), which is a single-view text-driven editing technique based on 3D Gaussian Splatting (3DGS). Specifically, in response to text instructions, we introduce a single-view editing strategy grounded in multi-view diffusion models, which reconstructs 3D scenes by leveraging only those views that yield consistent editing results. Additionally, we employ sparse 3D Gaussian Splatting as the 3D representation, which significantly enhances editing efficiency. We conducted a comparative analysis of SVGS against existing baseline methods across various scene settings, and the results indicate that SVGS outperforms its counterparts in both editing capability and processing speed, representing a significant advancement in 3D editing technology. For further details, please visit our project page at: https://amateurc.github.io/svgs.github.io/ .

The automatic design of a 3D tooth model plays a crucial role in dental digitization. However, current approaches face challenges in compositional 3D tooth generation because both the layouts and shapes of missing teeth need to be optimized. In addition, collision conflicts are often omitted in 3D Gaussian-based compositional 3D generation, where objects may intersect with each other due to the absence of explicit geometric information on the object surfaces. Motivated by graph generation through diffusion models and collision detection using 3D Gaussians, we propose an approach named DM-CFO for compositional tooth generation, where the layout of missing teeth is progressively restored during the denoising phase under both text and graph constraints. Then, the Gaussian parameters of each layout-guided tooth and the entire jaw are alternately updated using score distillation sampling (SDS). Furthermore, a regularization term based on the distances between the 3D Gaussians of neighboring teeth and the anchor tooth is introduced to penalize tooth intersections. Experimental results on three tooth-design datasets demonstrate that our approach significantly improves the multiview consistency and realism of the generated teeth compared with existing methods.

Convolutional neural networks are widely used for light field disparity estimation. However, many state-of-the-art deep learning models are computationally expensive due to their reliance on standard convolutions with varying kernel sizes. In this paper, we analyze the effect of various advanced convolution operations with different kernel sizes for feature extraction in a state-of-the-art light field disparity estimation network. Based on this investigation, we propose an optimized mixed convolution layer to extract relevant features using multiple kernel sizes in parallel, while maintaining significantly lower computational cost. Experimental results demonstrate that our approach reduces model complexity by up to 4.2× while also improving disparity estimation accuracy. These findings make the proposed convolutional operation more practical for light field applications, where efficient spatial and angular feature extraction is essential for improved model performance.

We formalize compressed sensing image reconstruction as an optimization problem, incorporating penalization of the spectral representation of images. Leveraging the original formulation of the Alternating Direction Method of Multipliers (ADMM), we introduce the innovative 3F-PnP algorithm. This algorithm integrates three filters: two deep learning neural network-based filters and the spectral BM3D denoiser, implemented through plug-and-play modules. Additionally, we show that the partial solutions of the ADMM optimization correspond precisely to the analysis and synthesis stages of the BM3D filter. Through numerical comparative analysis against ten state-of-the-art methods, we demonstrate the superiority of our algorithm in terms of improved accuracy and faster convergence rates.

This paper addresses the challenge of regularization in lensless single-shot phase retrieval (PR) by noise suppression. Due to the unique aspects of the PR algorithm, the noise is spatially correlated with a non-stationary level and distribution, which complicates PR’s reconstruction and convergence. To address this problem, We propose an algorithm for noise suppression, which utilizes the PIXPNet network for the initial estimation of noise parameters and prefiltering noise associated with the heavy tails of the noise distribution. Subsequently, the DRUNet network is applied within frequency sub-bands to suppress the noise meticulously. Our findings reveal that the proposed regularization, operating in a fully blind mode, outperforms our previous PR algorithm by achieving more effective noise suppression, enlarged field of view, and enhanced accuracy in estimating the height map of the object.

The hyperspectral broadband phase retrieval is developed for a scenario where both object and modulation phase masks are spectrally varying. The proposed iterative algorithm is based on a complex domain version of the alternating direction method of multipliers (ADMM) and the novel Spectral Proximity Operators derived for Gaussian and Poissonian multiple intensity observations. These proximity operators solve two problems. First, the complex-domain spectral components of the object are extracted from the total intensity observations calculated as the sums of the spectral intensities of diffractive patterns. Second, noisy observations are filtered, compromising noisy intensity observations and their predicted counterparts. The simulation and physical tests confirm that the broadband hyperspectral phase retrieval in the proposed formulation can be successfully resolved.

The volumetric representation of human interactions is one of the fundamental domains in the development of immersive media productions and telecommunication applications. Particularly in the context of the rapid advancement of Extended Reality (XR) applications, this volumetric data has proven to be an essential technology for future XR elaboration. In this work, we present a new multimodal database to help advance the development of immersive technologies. Our proposed database provides ethically compliant and diverse volumetric data, in particular 27 participants displaying posed facial expressions and subtle body movements while speaking, plus 11 participants wearing head-mounted displays (HMDs). The recording system consists of a volumetric capture (VoCap) studio, including 31 synchronized modules with 62 RGB cameras and 31 depth cameras. In addition to textured meshes, point clouds, and multi-view RGB-D data, we use one Lytro Illum camera for providing light field (LF) data simultaneously. Finally, we also provide an evaluation of our dataset employment with regard to the tasks of facial expression classification, HMDs removal, and point cloud reconstruction. The dataset can be helpful in the evaluation and performance testing of various XR algorithms, including but not limited to facial expression recognition and reconstruction, facial reenactment, and volumetric video. HEADSET and its all associated raw data and license agreement will be publicly available for research purposes.

Recent deep learning-based light field disparity estimation algorithms require millions of parameters, which demand high computational cost and limit the model deployment. In this paper, an investigation is carried out to analyze the effect of depthwise separable convolution and ghost modules on state-of-the-art EPINET architecture for disparity estimation. Based on this investigation, four convolutional blocks are proposed to make the EPINET architecture a fast and light-weight network for disparity estimation. The experimental results exhibit that the proposed convolutional blocks have significantly reduced the computational cost of EPINET architecture by up to a factor of 3.89, while achieving comparable disparity maps on HCI Benchmark dataset.

A problem of image denoising, when images are corrupted by a non-stationary noise, is considered in this paper. Since, in practice, no a priori information on noise is available, noise statistics should be pre-estimated prior to image denoising. In this paper, deep convolutional neural network (CNN) based method for estimation of a map of local, patch-wise, standard deviations of noise (so-calledsigma-map) is proposed. It achieves the state-of-the-art performance in accuracy of estimation of sigma-map for the case of non-stationary noise, as well as estimation of a noise variance for the case of an additive white Gaussian noise. Extensive experiments on image denoising using estimated sigma-maps demonstrate that our method outperforms recent CNN-based blind image denoising methods by up to 6 dB in PSNR, as well as other state-of-the-art methods based on sigma-map estimation by up to 0.5 dB, providing, at the same time, better usage flexibility. A comparison with the ideal case, when denoising is applied using ground-truth sigma-map, shows that a difference of corresponding PSNR values for the most of noise levels is within 0.1-0.2 dB, and does not exceed 0.6 dB.

Image denoising, demosaicing and super-resolution are key problems of image restoration well studied in the recent decades. Often, in practice, one has to solve these problems simultaneously. A problem of finding a joint solution of the multiple image restoration tasks just begun to attract an increased attention of researchers. In this paper, we propose an end-to-end solution for the joint demosaicing, denoising and super-resolution based on a specially designed deep convolutional neural network (CNN). We systematically study different methods to solve this problem and compared them with the proposed method. Extensive experiments carried out on large image datasets demonstrate that our method outperforms the state-of-the-art both quantitatively and qualitatively. Finally, we have applied various loss functions in the proposed scheme and demonstrate that by using the mean absolute error as a loss function, we can obtain superior results in comparison to other cases.

Hyperspectral (HS) imaging retrieves information from data obtained across a wide spectral range of spectral channels. The object to reconstruct is a 3D cube, where two coordinates are spatial and third one is spectral. We assume that this cube is complex-valued, i.e. characterized spatially frequency varying amplitude and phase. The observations are squared magnitudes measured as intensities summarized over spectrum. The HS phase retrieval problem is formulated as a reconstruction of the HS complex-valued object cube from Gaussian noisy intensity observations. The derived iterative algorithm includes the original proximal spectral analysis operator and the sparsity modeling for complex-valued 3D cubes. The efficiency of the algorithm is confirmed by simulation tests.

Natural images may contain regions with different levels of blur affecting image visual quality. No-reference image visual quality metrics should be able to effectively evaluate both blur and sharpness levels on a given image. In this paper, we propose a large image database BlurSet to verify this ability. BlurSet contains 5000 grayscale images of size 128×128 pixels with different levels of Gaussian blur and unsharp mask. For each image, a scalar value indicating the level of blur and the level of sharpness is provided. Several image quality assessment criteria are presented to evaluate how a given metric can estimate the level of blur/sharpness on BlurSet. An extensive comparative analysis of different no-reference metrics is carried out. Reachable levels of the quality criteria are evaluated using the proposed blur/sharpness convolutional neural network (BSCNN).

For training of no-reference image visual quality metrics large specialized image databases are used. For images of the databases mean opinion scores (MOS) are experimentally obtained collecting judgments of many observers. MOS of a given image reflects an averaged human perception of visual quality of the image. Each database has its own unknown scale of MOS values depending on unique content of the database. For training of no-reference metrics based on convolutional networks usually only one selected database is used, because all MOS values on input of training loss function should be in the same scale. In this paper, a simple and effective method of merging of several large databases into one database with transforming of their MOS into one scale is proposed. Accuracy of the proposed method is analyzed. Merged MOS is used for practical training of no-reference metric. Better effectiveness of the training is shown in comparative analysis.

The authors consider the problem of compressive sensed video recovery via iterative thresholding algorithm. Traditionally, it is assumed that some fixed sparsifying transform is applied at each iteration of the algorithm. In order to improve the recovery performance, at each iteration the thresholding could be applied for different transforms in order to obtain several estimates for each pixel. Then the resulting pixel value is computed based on obtained estimates using simple averaging. However, calculation of the estimates leads to significant increase in reconstruction complexity. Therefore, the authors propose a heuristic approach, where at each iteration only one transform is randomly selected from some set of transforms. First, they present simple examples, when block‐based 2D discrete cosine transform is used as the sparsifying transform, and show that the random selection of the block size at each iteration significantly outperforms the case when fixed block size is used. Second, building on these simple examples, they apply the proposed approach when video block‐matching and 3D filtering (VBM3D) is used for the thresholding and show that the random transform selection within VBM3D allows to improve the recovery performance as compared with the recovery based on VBM3D with fixed transform.

In this work we investigate the practicability of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems, such as space-varying image deblurring. Such algorithms have been shown in machine learning literature to have optimal complexities in theory, and provide great improvement empirically over the full gradient methods. Surprisingly, in some tasks such as image deblurring, many of such methods fail to converge faster than the accelerated full gradient method (FISTA), even in terms of epoch counts. We investigate this phenomenon and propose a theory-inspired mechanism to characterize whether a given inverse problem should be preferred to be solved by stochastic optimization technique with a known sampling pattern. Furthermore, to overcome another key bottleneck of stochastic optimization which is the heavy computation of proximal operators while maintaining fast convergence, we propose an accelerated primal-dual SGD algorithm and demonstrate the effectiveness of our approach in image deblurring experiments.

This paper studies the problem of full reference visual quality assessment of denoised images with a special emphasis on images with low contrast and noise-like texture. Denoising of such images together with noise removal often results in image details loss or smoothing. A new test image database, FLT, containing 75 noise-free `reference' images and 300 filtered (`distorted') images is developed. Each reference image, corrupted by an additive white Gaussian noise, is denoised by the BM3D filter with four different values of threshold parameter (four levels of noise suppression). After carrying out a perceptual quality assessment of distorted images, the mean opinion scores (MOS) are obtained and compared with the values of known full reference quality metrics. As a result, the Spearman Rank Order Correlation Coefficient (SROCC) between PSNR values and MOS has a value close to zero, and SROCC between values of known full-reference image visual quality metrics and MOS does not exceed 0.82 (which is reached by a new visual quality metric proposed in this paper). The FLT dataset is more complex than earlier datasets used for assessment of visual quality for image denoising. Thus, it can be effectively used to design new image visual quality metrics for image denoising.

Images of different origin contain textures, and textural features in such regions are frequently employed in pattern recognition, image classification, information extraction, etc. Noise often present in analyzed images might prevent a proper solution of basic tasks in the aforementioned applications and is worth suppressing. This is not an easy task since even the most advanced denoising methods destroy texture in a more or less degree while removing noise. Thus, it is desirable to predict the filtering behavior before any denoising is applied. This paper studies the efficiency of texture image denoising for different noise intensities and several filter types under different visual quality criteria (quality metrics). It is demonstrated that the most efficient existing filters provide very similar results. From the obtained results, it is possible to generalize and employ the prediction strategy earlier proposed for denoising techniques based on the discrete cosine transform. Accuracy of such a prediction is studied and the ways to improve it are considered. Some practical recommendations concerning a decision to undertake whether it is worth applying a filter are given.

We introduce a paradigm for nonlocal sparsity reinforced deep convolutional neural network denoising. It is a combination of a local multiscale denoising by a convolutional neural network (CNN) based denoiser and a nonlocal denoising based on a nonlocal filter (NLF), exploiting the mutual similarities between groups of patches. CNN models are leveraged with noise levels that progressively decrease at every iteration of our framework, while their output is regularized by a nonlocal prior implicit within the NLF. Unlike complicated neural networks that embed the nonlocality prior within the layers of the network, our framework is modular, and it uses standard pretrained CNNs together with standard nonlocal filters. An instance of the proposed framework, called NN3D, is evaluated over large grayscale image datasets showing state-of-the-art performance.

Single image super-resolution (SISR) is an ill-posed problem aiming at estimating a plausible high-resolution (HR) image from a single low-resolution image. Current state-of-the-art SISR methods are patch-based. They use either external data or internal self-similarity to learn a prior for an HR image. External data-based methods utilize a large number of patches from the training data, while self-similarity-based approaches leverage one or more similar patches from the input image. In this paper, we propose a self-similarity-based approach that is able to use large groups of similar patches extracted from the input image to solve the SISR problem. We introduce a novel prior leading to the collaborative filtering of patch groups in a 1D similarity domain and couple it with an iterative back-projection framework. The performance of the proposed algorithm is evaluated on a number of SISR benchmark data sets. Without using any external data, the proposed approach outperforms the current non-convolutional neural network-based methods on the tested data sets for various scaling factors. On certain data sets, the gain is over 1 dB, when compared with the recent method A+. For high sampling rate (x4), the proposed method performs similarly to very recent state-of-the-art deep convolutional network-based approaches.

This letter is devoted to the problem of rotation invariant texture classification. Novel rotation invariant feature, symmetric dense microblock difference (SDMD), is proposed which captures the information at different orientations and scales. N-fold symmetry is introduced in the feature design configuration, while retaining the random structure that provides discriminative power. The symmetry is utilized to achieve a rotation invariance. The SDMD is extracted using an image pyramid and encoded by the Fisher vector approach resulting in a descriptor which captures variations at different resolutions without increasing the dimensionality. The proposed image representation is combined with the linear SVM classifier. Extensive experiments are conducted on four texture data sets [Brodatz, UMD, UIUC, and Flickr material data set (FMD)] using standard protocols. The results demonstrate that our approach outperforms the state of the art in texture classification. The MATLAB code is made available.

This paper is devoted to the problem of texture classification. Motivated by recent advancements in the field of compressive sensing and keypoints descriptors, a set of novel features called dense micro-block difference (DMD) is proposed. These features provide highly descriptive representation of image patches by densely capturing the granularities at multiple scales and orientations. Unlike most of the earlier work on local features, the DMD does not involve any quantization, thus retaining the complete information. We demonstrate that the DMD have dimensionality much lower than Scale Invariant Feature Transform (SIFT) and can be computed using integral image much faster than SIFT. The proposed features are encoded using the Fisher vector method to obtain an image descriptor, which considers high-order statistics. The proposed image representation is combined with the linear support vector machine classifier. Extensive experiments are conducted on five texture data sets (KTH-TIPS, UMD, KTH-TIPS-2a, Brodatz, and Curet) using standard protocols. The results demonstrate that our approach outperforms the state-of-the-art in texture classification.

This paper describes a recently created image database, TID2013, intended for evaluation of full-reference visual quality assessment metrics. With respect to TID2008, the new database contains a larger number (3000) of test images obtained from 25 reference images, 24 types of distortions for each reference image, and 5 levels for each type of distortion. Motivations for introducing 7 new types of distortions and one additional level of distortions are given; examples of distorted images are presented. Mean opinion scores (MOS) for the new database have been collected by performing 985 subjective experiments with volunteers (observers) from five countries (Finland, France, Italy, Ukraine, and USA). The availability of MOS allows the use of the designed database as a fundamental tool for assessing the effectiveness of visual quality. Furthermore, existing visual quality metrics have been tested with the proposed database and the collected results have been analyzed using rank order correlation coefficients between MOS and considered metrics. These correlation indices have been obtained both considering the full set of distorted images and specific image subsets, for highlighting advantages and drawbacks of existing, state of the art, quality metrics. Approaches to thorough performance analysis for a given metric are presented to detect practical situations or distortion types for which this metric is not adequate enough to human perception. The created image database and the collected MOS values are freely available for downloading and utilization for scientific purposes.

The paper addresses interferometric phase image estimation, that is, the estimation of phase modulo-2π images from sinusoidal 2π-periodic and noisy observations. These degradation mechanisms make interferometric phase image estimation a challenging problem. We tackle this challenge by reformulating the true estimation problem as a sparse regression in the complex domain. Following the standard procedure in patch-based image restoration, the image is partitioned into small overlapping square patches. BM3D algorithm equipped with high order SVD (HOSVD) is used to form complex domain frames suitable to sparse representations of the complex-valued data. HOSVD applied to the groups of BM3D data enables the design of spatially variant and data adaptive orthonormal complex domain transforms. The effectiveness of the new sparse coding based approach to interferometric phase estimation, termed Interferometric PHASE via Block matching and High order SVD (InPHASE-BHS) is illustrated in a series of simulation experiments where it outperforms the state-of-the-art.

We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d-dimensional patches are stacked together in a (d+1)-dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D "group." The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction.

This paper is dedicated to fast video coding based on three-dimensional discrete wavelet transform. First, we propose a novel low-complexity bit-plane entropy coding of wavelet subbands based on Levenstein zero-run coder for low entropy contexts and adaptive binary range coder for other contexts. Second, we propose a rate-distortion efficient criterion for skipping 2-D wavelet transforms and entropy encoding based on parent-child subband tree. Finally, we propose one pass rate control which uses virtual buffer concept for adaptive Lagrange multiplier selection. Simulations results show that the proposed video codec has a much lower computational complexity (from 2 to 6 times) for the same quality level compared to the H.264/AVC standard in the low complexity mode.

A new block-based multi-metric fusion (BMMF) approach is proposed for perceptual image quality assessment. The proposed BMMF scheme automatically detects image content and distortion types in a block via machine learning, which is motivated by the observation that the performance of an image quality metric is highly influenced by these factors. Locally, image block content is classified into three types; namely, smooth, edge and texture. Image distortion is detected and grouped into five types. An appropriate image quality metric is adopted for each block by considering its content and distortion types, and then all block-based quality metrics are fused to result in one final score. Furthermore, a corrected version of BMMF is derived for a specific group of distortions based on image complexity analysis. The proposed BMMF scheme is tested on TID database with its Spearman Correlation equal to 0.9471, which outperforms today's state-of-the-art image quality metrics.

In this paper we propose a novel efficient adaptive binary arithmetic coder which is multiplication-free and requires no look-up tables. To achieve this, we combine the probability estimation based on a virtual sliding window with the approximation of multiplication and the use of simple operations to calculate the next approximation after the encoding of each binary symbol. We show that the proposed algorithm is faster and provides a better compression efficiency compared to the M-coder in the CABAC entropy coding scheme of the H.264/AVC video coding standard.

A JPEG-based perceptual image coder is proposed in this work, where a block-based image quality metric is used to optimize the rate-quality (RQ) performance. Under this framework, the quality of each image block is measured using a local quality metric while the overall image quality is evaluated by summing up all local quality metrics. A rate-quality optimization (RQO) problem is formulated in each macroblock of size 16×16 based on its associated empirical RQ curve. Then, to achieve the best perceptual image quality under a given bit budget constraint, the set of optimal quantization parameters (QPs) for image blocks is solved using the Lagrangian approach. It is demonstrated that the proposed perceptual image codec offers a significant improvement over the JPEG baseline in both subjective and objective evaluations.

A family of the block matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling , . In this paper, we construct analysis and synthesis frames, formalizing BM3D image modeling, and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem, i.e., one given by the minimization of the single-objective function and another based on the generalized Nash equilibrium (GNE) balance of two objective functions. The latter results in the algorithm where deblurring and denoising operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the GNE formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.

We propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering, where a higher dimensional transform-domain representation of the observations is leveraged to enforce sparsity, and thus regularize the data: 3-D spatiotemporal volumes are constructed by tracking blocks along trajectories defined by the motion vectors. Mutually similar volumes are then grouped together by stacking them along an additional fourth dimension, thus producing a 4-D structure, termed group, where different types of data correlation exist along the different dimensions: local correlation along the two dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation (i.e., self-similarity) along the fourth dimension of the group. Collaborative filtering is then realized by transforming each group through a decorrelating 4-D separable transform and then by shrinkage and inverse transformation. In this way, the collaborative filtering provides estimates for each volume stacked in the group, which are then returned and adaptively aggregated to their original positions in the video. The proposed filtering procedure addresses several video processing applications, such as denoising, deblocking, and enhancement of both grayscale and color data. Experimental results prove the effectiveness of our method in terms of both subjective and objective visual quality, and show that it outperforms the state of the art in video denoising.

The paper contains comparisons of lower bound (potential) and achieved efficiency for filtering grayscale and color images corrupted by AWGN. It is demonstrated that for complex structure images the corresponding limits are practically reached. Then, the main problems of the current stage of filter design are discussed taking into account noise models more adequate for practice, inherent properties of multicomponent (e.g. color, hyperspectral, etc.) images, and other qualitative criteria than conventional MSE or PSNR criteria.

In this paper, we present a novel stereoscopic video quality assessment method based on 3D-DCT transform. In our approach, similar blocks from left and right views of stereoscopic video frames are found by block-matching, grouped into 3D stack and then analyzed by 3D-DCT. Comparison between reference and distorted images are made in terms of MSE calculated within the 3D-DCT domain and modified to reflect the contrast sensitive function and luminance masking. We validate our quality assessment method using test videos annotated with results from subjective tests. The results show that the proposed algorithm outperforms current popular metrics over a wide range of distortion levels.

Recently within the framework of nonlocal patch-wise estimation a family of the Block Matching 3-D (BM3D) algorithms has been developed for various imaging problems [1], [2]. In [3] we demonstrated that BM3D modeling allows frame interpretation and constructed the corresponding analysis and synthesis frames which we call BM3D-frames. In this paper we use the BM3D-frames to develop an image deblurring algorithm based on the alternating optimization of two objective functions corresponding to decoupled denoising and deblurring operations. Compared to the standard approach based on minimization of a single objective function, decoupling allows to achieve both better reconstruction performance and essential simplification of the algorithm. Simulated experiments demonstrate numerical and visual superiority of the proposed algorithm over the current state-of-the-art methods confirming the advantage of the BM3D-frames as an image modeling tool.

In this paper we present a new near lossless reversible watermarking algorithm using adaptive prediction for embedding. The prediction is based on directional first-order differences of pixel intensities within a suitably selected neighborhood. The proposed scheme results to be computationally efficient and allows achieving high embedding capacity while preserving a high image quality. Extensive experimental results demonstrate the effectiveness of the proposed approach.

An algorithm for the blind separation of mutually independent and/or temporally correlated sources is presented in this letter. The algorithm is closely related to the maximum likelihood approach based on entropy rate minimization but uses a simpler contrast function that can be accurately and efficiently estimated using nearest-neighbor distances. The advantages of the new algorithm are highlighted using simulations and real electroencephalographic data.

In estimation of the efficiency for lossy image compression methods, standard sets of test images are commonly used. This allows the comparison of new techniques to existing methods without having to actually implement the existing technique. However, this does not allow adequate evaluation of the performance of the methods for compressing natural images. In this paper, we analyze the efficiency of a set of lossy compression techniques (JPEG, JPEG2000, HD Photo and ADCTC) using a set of images obtained by three consumer quality digital cameras.

In this contribution, a new image database for testing full-reference image quality assessment metrics is presented. It is based on 1700 test images (25 reference images, 17 types of distortions for each reference image, 4 levels for each type of distortion). Using this image database, 654 observers from three different countries (Finland, Italy, and Ukraine) have carried out about 400000 individual human quality judgments (more than 200 judgments for each distorted image). The obtained mean opinion scores for the considered images can be used for evaluating the performances of visual quality metrics as well as for comparison and for the design of new metrics. The database, with testing results, is freely available.

We present a simple and usable noise model for the raw-data of digital imaging sensors. This signal-dependent noise model, which gives the pointwise standard-deviation of the noise as a function of the expectation of the pixel raw-data output, is composed of a Poissonian part, modeling the photon sensing, and Gaussian part, for the remaining stationary disturbances in the output data. We further explicitly take into account the clipping of the data (over- and under-exposure), faithfully reproducing the nonlinear response of the sensor. We propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image. Experiments with synthetic images and with real raw-data from various sensors prove the practical applicability of the method and the accuracy of the proposed model.

The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (HCI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval [-pi, pi] and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the HCI adaptation algorithm.

We propose an effective color image denoising method that exploits filtering in highly sparse local 3D transform domain in each channel of a luminance-chrominance color space. For each image block in each channel, a 3D array is formed by stacking together blocks similar to it, a process that we call "grouping". The high similarity between grouped blocks in each 3D array enables a highly sparse representation of the true signal in a 3D transform domain and thus a subsequent shrinkage of the transform spectra results in effective noise attenuation. The peculiarity of the proposed method is the application of a "grouping constraint" on the chrominances by reusing exactly the same grouping as for the luminance. The results demonstrate the effectiveness of the proposed grouping constraint and show that the developed denoising algorithm achieves state-of-the-art performance in terms of both peak signal-to-noise ratio and visual quality.

We introduce a new approach to image reconstruction from highly incomplete data. The available data are assumed to be a small collection of spectral coefficients of an arbitrary linear transform. This reconstruction problem is the subject of intensive study in the recent field of "compressed sensing" (also known as "compressive sampling"). Our approach is based on a quite specific recursive filtering procedure. At every iteration the algorithm is excited by injection of random noise in the unobserved portion of the spectrum and a spatially adaptive image denoising filter, working in the image domain, is exploited to attenuate the noise and reveal new features and details out of the incomplete and degraded observations. This recursive algorithm can be interpreted as a special type of the Robbins-Monro stochastic approximation procedure with regularization enabled by a spatially adaptive filter. Overall, we replace the conventional parametric modeling used in CS by a nonparametric one. We illustrate the effectiveness of the proposed approach for two important inverse problems from computerized tomography: Radon inversion from sparse projections and limited-angle tomography. In particular we show that the algorithm allows to achieve exact reconstruction of synthetic phantom data even from a very small number projections. The accuracy of our reconstruction is in line with the best results in the compressed sensing field.

This letter presents an advanced discrete cosine transform (DCT)-based image compression method that combines advantages of several approaches. First, an image is divided into blocks of different sizes by a rate-distortion-based modified horizontal-vertical partition scheme. Statistical redundancy of quantized DCT coefficients of each image block is reduced by a bit-plane dynamical arithmetical coding with a sophisticated context modeling. Finally, a post-filtering removes blocking artifacts in decompressed images. The proposed method provides significantly better compression than JPEG and other DCT-based techniques. Moreover, it outperforms JPEG2000 and other wavelet-based image coders

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

The shape-adaptive discrete cosine transform ISA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation-Intersection of Confidence Intervals technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region's statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.

In our recent work, a class of parametric transforms, including family of Haar-like transforms, was introduced and studied in application to image compression. Parametric Haar-like transform (PHT) is a discrete orthogonal transform such that it may be computed with a fast algorithm in a structure similar to that of classical fast Haar transform and such that its matrix contains arbitrary predefined vector in its first row. The aim of this paper is to study a potential use of parametric Haar-like transforms in image denoising. A PHT-based post-processing method is proposed which may improve a denoising method based on fixed transforms. In particular, it is shown that the proposed method may significantly improve the performance of wavelet thresholding based image denoising.

In this paper we propose a computationally efficient method for image super-resolution reconstruction. We concentrate on pure translational motion and shift-invariant blur. This is the case of interlaced sampling where each low resolution image is uniformly sampled but the overall sampling is non-uniform with respect to the high resolution grid. The reconstruction problem is considered in a multi-resolution framework using separable B-spline wavelets as basis. This allows performing the reconstruction on a uniform higher resolution grid by digital filtering. A computationally efficient structure-the transposed modified Farrow structure is used to achieve a near least squares solution without using any matrix inversions or iterations. The reconstruction can also be performed at non-dyadic scales. Our method minimizes the aliasing distortions and gives results comparable with other least squares techniques.

The application of adaptive techniques for obtaining bispectrum estimates in additive Gaussian noise and random shifts of received signals is considered. An approach using joint adaptive robust forming of bispectrum estimates and processing of complex-valued signal Fourier spectrum estimates by discrete cosine transform-based filtering with local variance estimation within each block is proposed. The advantages of the proposed approach in comparison to the conventional signal waveform recovery from bispectrum are illustrated by computer simulations

We present a method based on the matching pursuits algorithm for the extraction of time-frequency features that can be used for classification of various abnormal heartbeats. Further, we investigate the usefulness of independent component analysis for extracting additional spatial features from multichannel electrocardiographic recordings. The performance of these two different sets of features is assessed using the 48 recordings of the MIT-BIH arrhythmia database.

We propose an approach to fractal image compression that provides fast decoding of the compressed image in one iteration and allows knowing the accurate value of the error contributed by each range block to the collage error at each step of partition scheme optimization. A modification of this method assuming equal sizes of domain and range blocks is considered. The results of the proposed approach application to test images are analyzed. The further research directions are discussed.

A spatially adaptive image deblurring algorithm is presented for Poisson observations. It adapts to the unknown image smoothness by using local polynomial approximation (LPA) kernel estimates of varying scale and direction based on the intersection of confidence intervals (ICI) rule. The signal-dependant characteristics of the Poissonian noise are exploited to accurately compute the pointwise variances of the directional estimates. The results show that this accurate pointwise adaptive algorithm significantly improves the image restoration quality.

We propose a novel nonparametric regression metthod for deblurring noisy images. The method is based on the local polynomial approximation (LPA) of the image and the paradigm of intersecting confidence intervals (ICI) that is applied to define the adaptive varying scales (window sizes) of the LPA estimators. The LPA-ICI algorithm is nonlinear and spatially adaptive with respect to smoothness and irregularities of the image corrupted by additive noise. Multiresolution wavelet algorithms produce estimates which are combined from different scale projections. In contrast to them, the proposed ICI algorithm gives a varying scale adaptive estimate defining a single best scale for each pixel. In the new algorithm, the actual filtering is performed in signal domain while frequency domain Fourier transform operations are applied only for calculation of convolutions. The regularized inverse and Wiener inverse filters serve as deblurring operators used jointly with the LPA-design directional kernel filters. Experiments demonstrate the state-of-art performance of the new estimators which visually and quantitatively outperform some of the best existing methods.

The computational complexity and memory load of the adaptive finite impulse response (AFIR) filter are significant for a large filter size. The adaptive interpolated FIR (AIFIR) filter, which uses a sparse adaptive filter followed by an interpolator, has been shown to be a better alternative. However, when the AIFIR filter is implemented, the coefficients of the interpolator must be designed in advance based on prior information about the application at hand. Such information is not always available and the design of a proper interpolator is sometimes difficult. In this paper we introduce a new structure called double adaptive interpolated FIR (DAIFIR) filter in which the fixed interpolator is replaced by an adaptive filter of the same length. We show by means of simulations that the behavior of the proposed structure is close to the behavior of the AIFIR having a proper designed interpolator. In situations in which a fixed interpolator cannot be designed in advance the DAIFIR might be a good alternative.

Forcing functions represent an important class of Boolean functions that have been extensively studied in the analysis of the dynamics of random Boolean networks as models of genetic regulatory systems. Several other so-called Post classes of Boolean functions are closely related to forcing functions and have been used in learning theory as well as in control systems. We develop novel spectral algorithms to test membership of a Boolean function in these classes. These algorithms are highly efficient and are essential in learning problems, especially in the context of genetic regulatory networks, where the same learning procedures are applied repeatedly.

Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the image during filtering, all noisy pixels must be detected. Then only these detected pixels must be corrected. We present in this paper two solutions to the edge preservation problem. The first one is an impulse detector. This detector is based on a comparison of signal samples within a narrow rank window. It is quite efficient for precise detection of impulses in images corrupted by impulsive noise with a low corruption rate. The second solution is based on threshold Boolean filtering, when the binary slices of an image, obtained by the threshold decomposition, are processed by original Boolean functions.

This paper introduces an image decimation technique based on the use of a near least-squares criterion that makes a proper compromise between the L/sub 2/ and l/sub 2/ norm minimization cases. The theory of orthogonal projections is related to the derivation of a computationally efficient decimation structure possessing good antialiasing properties. It is shown how this structure can be realized by the transposed Farrow structure when using piece-wise polynomial basis functions. It is shown, by means of examples, that with a considerably lower computational complexity the proposed structure provides practically the same quality for the restored images as the best existing structures.

A new algorithm of the block encoding that can be implemented in such a way that block of several letters is coded using almost the same number of operations as a usual code uses for one letter is suggested. The new algorithm is based on methods of grouping of alphabet letters suggested recently in B. Ryabko, J. Astola (2003), B. Ryabko, J. Rissanen (2003) which combines letters from a large alphabet into a small number of subsets without an essential increase of the code redundancy.

Summary form only given. An approach based on applying Delaunay triangulation to compression of mean values of image blocks that have non-identical shape and size is proposed. It can be useful for image compression methods that require the use of image partition schemes with non-equal block size like fractal and DCT-based image coding. Several methods of block mean value coding are considered. In particular, the drawbacks of using quantization with further redundancy elimination by entropy coders are discussed. Another considered method is the forming of the block mean value image and its further compression by lossy coders. Finally, the motivations in favor of Delaunay triangulation application to block mean value image coding are presented.

The order statistic least mean square (OSLMS) algorithm is a modification of the least mean square (LMS) algorithm, that uses an order statistic (OS) filtering operation to the gradient estimates. There are many OS filters that can be applied to the gradient estimates and each of them is optimal for a certain gradient distribution. In this paper a new OSLMS algorithm is introduced, permitting an automatic selection of the “optimal” OS filter. In this algorithm, an adaptive L filter is employed for filtering the gradient. Simulations conducted in a system identification framework show the improvements of the new algorithm comparing with known OSLMS algorithms.

A method for electromyogram (EMG) artifact suppression in electrocardiogram (ECG) recordings is presented. In an attempt to improve the traditional compromise between efficient EMG artifact suppression and preservation of the ECG waveform, the method combines a dynamic approximation filtering working in the QRS complexes areas, with a transform domain denoising of the segments outside them. The switching between the two procedures is controlled by the ECG signal slew rate. The results obtained show a virtual preservation of the QRS amplitudes and a considerable reduction of the EMG artifact.

We introduce a new transform domain (least mean square) LMS algorithm with variable step. The existing approaches use different time-variable step-sizes for each filter tap. The step-sizes are time-variable due to the power estimates of each transform coefficient. In our new approach, for each step-size we define a local component that is given by the power normalization, and a global component that is the same for each filter coefficient. We show that if the global component is also made time-variable, depending on the output error, the speed of convergence can be significantly improved.

An algorithm for image noise-removal based on local adaptive window size filtering is developed. Two features for use in local spatial/transform-domain filtering are suggested. First, filtering is performed on images corrupted not only by additive white noise, but also by image-dependent (e.g. film-grain noise) or multiplicative noise. Second, the used transforms are equipped with a varying adaptive window size obtained by the intersection of confidence intervals (ICI) rule. Finally, we combine all estimates available for each pixel from neighboring overlapping windows by weighted averaging these estimates. Comparison of the algorithm with the known techniques for noise removal from images shows the advantage of the new algorithm, both quantitatively and visually.

An edge-preserving method for image resizing (decimation and interpolation) is proposed. The decimation is considered as an orthogonal projection with respect to the chosen interpolation basis. The latter one is formed in a spline-like manner as a linear combination of B-splines of different degrees. This combination is optimized in such a way that the small image details are preserved. Considering the strongest edges as step edges, a segmentation procedure preceding the decimation is proposed. It leads to resized images with clearly outlined borders.

A subband decomposition based lossless image compression algorithm based on adaptive methods is described. The decomposition is achieved by a two-channel adaptive filter bank. The resulting coefficients are lossy coded first, and then the residual error between the lossy and error free coefficients are compressed. The locations and the magnitudes of the nonzero coefficients are encoded separately by a hierarchical enumerative coding method. The locations of the nonzero coefficients in child bands are predicted from those in the parent band. The proposed compression algorithm, on the average, provides higher compression ratios than the state-of-the-art methods.

Local adaptive image denoising in transform domain is a powerful tool for adapting to unknown smoothness of the images. We propose to perform local adaptive denoising with adaptively varying local transform support size rather than using a transform with fixed size. We use a special rule (intersection of confidence intervals-ICI) to select the optimum window sizes locally. The algorithm provides significant improvements in the de-noising performance.

A problem of speeding-up the fractal compression of still images is discussed. The techniques based on analysis of local variance for range blocks and domain blocks are proposed and considered. An algorithm for fast search of domain blocks corresponding to the range block in the best manner is described. It is shown that a reduction of search CPU time by several times can be provided and the obtained benefit depends upon the complexity of image to be compressed and the range block size. The proposed procedure for speeding up the fractal compression does not result in additional losses in recovered image quality.

In this work we study the harmonic analysis of functions on the n-D Heisenberg groups H over the Galois field GF(p) for generating Gabor atoms. Analogous to the Fourier transform, the expansion of functions on the basis of irreducible complex matrix representations of the Heisenberg group defines the generalized Fourier transform on this group, or, simply, the Fourier-Heisenberg transform. The fast algorithms for the n-D Fourier transforms on the Heisenberg and affine groups are developed in this paper. A general method of computing the Gabor distribution and wavelet transform based on the fast Fourier-Heisenberg-Weyl transform is also presented.

We propose to generate a library of median pyramidal decompositions organized as a tree. It is shown that the best decomposition on this tree can be chosen using the techniques developed in wavelet theory. Based on the tree of decompositions, a denoising algorithm is introduced. Numerical simulations have shown that the proposed algorithm is more effective for signal denoising than the method based on the traditional median pyramidal transform.

A new two-stage algorithm for electrocardiographic (EGG) signal denoising has been proposed. It combines wavelet shrinkage with Wiener filtering in the translation-invariant wavelet domain. A time-frequency dependent thresholding has been proposed and grounded for obtaining a more adequate signal estimate in the first stage of the algorithm. It is related to ECG signal morphology and hence outperforms other thresholding approaches in this area. The experiments carried out on pathological and normal ECGs have shown better algorithm capabilities in comparison with other thresholding algorithms while suppressing parasite electromyographic (EMG) signals (the noise) and preserving diagnostically important ECG signal features.

We propose an algorithm for compressing images corrupted by film-grain type noise. The algorithm nonlinearly modifies the transform coefficients of noisy data for reducing the impact of noise on compression. Although any orthogonal transform is suitable for the application, the orthogonal wavelet transform is preferred for simplicity in calculating the filter coefficients and for obtaining better compression performance. The algorithm is tested on different images at different noise variances and the results are compared to spatial filtering before compression. Our method outperforms spatial prefiltering in terms of PSNR values and it is easier to implement.

The K-nearest neighbor (K-NN) filter introduced by Davis and Rosenfeld (1978) has been long time successfully used in application to noise smoothing problems. The main drawback of this filter is its very high computational time. In this paper we introduce a slightly modified version of the K-NN filter and show that these two filters have practically the same performance in the noise removal sense while our modification is simpler in implementation. A binary-tree search technique for the implementation off the modified K-NN filter is presented, and an efficient bit-serial architecture for implementation of this filter is proposed.

We describe a novel approach to solve a problem of bandwidth selection for median filtering a signal given with an additive noise. The approach is based on the intersection of confidence intervals ICI rule and gives the algorithm, which is simple to implement and nearly ideal within lnN factor in the point-wise mean squared errors risk for estimating the signal. The ICI rule gives the adaptive varying bandwidths and enables the algorithm to be spatial adaptive in the sense that its quality is close to that which one could achieve if the smoothness of the estimated signal was known in advance.

We propose a method for the efficient encoding of the significance maps in wavelet-based image compression. Adopting the significance map encoding part of the morphology-based scheme, we introduce three new features: exploitation of the knowledge of coefficient magnitudes in the parent band; reordering of the residual part of the significance map; and the employment of hierarchical enumerative coding, a new entropy coding method, instead of arithmetic coding. Experimental results show that utilization of these features bring a consistent improvement. The average improvement is around 7.6%.

We propose a procedure for stack filter design that takes into consideration the filter's sample selection probabilities. A statistical optimization of stack filters can result in a class of stack filters, all of which are statistically equivalent. Such a situation arises in cases of nonsymmetric noise distributions or in the presence of constraints. Among the set of equivalent stack filters, our method constructs a statistically optimal stack filter whose sample selection probabilities are concentrated in the center of its window. This leads to improvement of detail preservation.

This paper describes a fast new n-D discrete Radon transform (DRT) and a fast exact inversion algorithm for it, without interpolating from polar to Cartesian coordinates of using the backprojection operator. The new approach is based on the fast Nussbaumer's (1982) polynomial transform (NPT).

There are various de-noising algorithms and optimization methods for different signal and noise characteristics. However, the signals used in real application may deviate from the model. For example: signal and/or noise may not be stationary or a proper model for them may nor be available. MCG (magnetocardiography) is an example signal, where conventional de-noising methods are not giving satisfactory results. Local adaptive processing allows to modify filtering parameters according to the specific properties of different "portions" of a signal. In this paper a methodology for adopting the transform domain local adaptive processing to the specific task of MCG signal de-noising is introduced.

A block-median pyramidal transform, based on the median operation over non-overlapping blocks and linear Lagrange interpolation, is considered for image denoising. In addition to the soft and hard thresholding schemes, other techniques are employed. Firstly, the partial cycle-spinning algorithm is used to achieve near translation invariance. Secondly, local adaptation in the transform domain is used for adjustment of parameters in accordance with spatial behavior of the image.

A local adaptive image de-noising method based on local selection of the best wavelet, among a finite set, within a sliding window at each level of decomposition is developed. The proposed method suggests certain advantages in terms of de-noising efficiency and detail preservation especially when the image includes different regions which may be efficiently represented by different bases or a priori information on the image is limited. This work concerns the method of using an adaptively varying base and the best wavelet selection rule. The method is implemented and comparative results are submitted.

In this letter, we provide a method for deriving the output distribution function of any recursive stack filter. In particular, we give the output distribution of the recursive median filter. The method used relies on finite automata and Markov chain theory. The distribution of any recursive stack filter is expressed as a vector multiplication of steady-state probabilities by the truth table vector of the Boolean function defining the filter.

Moment invariants have found many applications in pattern recognition. The main difficulty in the application of moment invariants is their computation. The presented paper is devoted to elaboration of new methods of image invariant recognition in Euclidean and non-Euclidean 2-, 3 and n-dimensional spaces, based on the theory of Clifford hypercomplex numbers that allow to work out efficient algorithms. Algebraic invariant pattern recognition has been discussed in the literature, however the Clifford algebra based method allows a more elegant reformulation providing greater geometrical insight.

Local transform domain nonlinear image filtering is studied in this work. Nonlinear filtering works in a moving window and several filtered outputs are obtained for each pixel from different windows. A second stage filtering is applied to those filtered outputs by cellular neural network with multivalued neurons. The simulation results are presented for additive Gaussian, Laplacian, and exponentially distributed noise corrupted images.

This paper is devoted to the theoretical analysis of the fitness function in genetic algorithms using wavelet packet (WP) transforms. More specifically, WP transforms are used to calculate the average fitness value of a schema. Based on this one can decide whether a certain function is easy or hard for a genetic algorithm. The result is an extension of Bethke's (1980) work who discovered an efficient method for calculating schema average fitness values using the Walsh transform.

Interpolation techniques are widely used in many applications of signal processing. This paper is devoted to synthesizing and efficiently implementing a class of generalized spline-interpolators. A new parametric class of generalized B-splines is introduced. It contains as special cases B-splines and alternative B-splines. In the most general case, the proposed spline functions can be represented as a linear combination of the weighted and shifted classic B-splines of different orders. The applicability of the resulting splines to discrete-time interpolation is investigated and compared to classical splines. Furthermore, the implementation of the discrete-time interpolation with the aid of efficient digital filter structures is considered in detail.

Stack filters can be approximated by using PCDOS-filters (permutation conditioned distance order statistic filters). Generalized selection probabilities are introduced in order to achieve even faster implementations for PCDOS-filters via using generalized orderings by stack filter banks. Theory and an algorithm for the practical use of the introduced method are provided. Some alternatives to the PCDOS-filter are also considered.

In the present work weighted Chow parameters are developed with the aim of their application in the statistical analysis of a class of nonlinear filters, namely stack filters, which are specified by positive Boolean functions (PBF) representing the binary output at each threshold level of the continuous-valued signal. Selection probabilities of stack filters were defined based on the fact that the output of a continuous stack filter is one of the samples within the input window. The notion of weighted Chow parameters is introduced in this paper for analysis and computation of the sample selection probability vector of a continuous stack filter.