In Compressive Sensing (CS) of sparse signals, standard$\ell_{1}$minimization can be effectively replaced with Weighted$\ell_{1}$-minimization$(\mathbf{W}\ell_{1})$if some information about the signal or its sparsity pattern is available. If no such information is available, Re-Weighted$\ell_{1}$-minimization$(\mathbf{ReW}\ell_{1})$can be deployed. ReW$\ell _{1}$solves a series of W$\ell_{1}$problems, and therefore, its computational complexity is high. An alternative to ReW$\ell_{1}$is the Greedy Pursuits Assisted Basis Pursuit (GPABP) which employs multiple Greedy Pursuits (GPs) to obtain signal information which in turn is used to run W$\ell_{1}$. Although GPABP is an effective fusion technique, it adapts a binary weighting strategy for running W$\ell_{1}$, which is very restrictive. In this article, we propose a gradual weighting strategy for W$\ell_{1}$, which handles the signal estimates resulting from multiple GPs more effectively compared to the binary weighting strategy of GPABP. The resulting algorithm is termed as Greedy Pursuits assisted Weighted$\ell_{1}$-minimization$(\mathbf{GP-W}\ell_{1})$. For GP-W$\ell_{1}$, we derive the theoretical upper bound on its reconstruction error. Through simulation results, we show that the proposed GP-W$\ell_{1}$outperforms ReW$\ell_{1}$and the state-of-the-art GPABP.

Distributed Compressive Sensing (DCS) is an extension of compressive sensing from single measurement vector problem to Multiple Measurement Vectors (MMV) problem. In DCS, several reconstruction algorithms have been proposed to reconstruct the joint-sparse signal ensemble. However, most of them are designed for signal ensemble sharing common support . Since the assumption of common sparsity pattern is very restrictive, we are more interested in signal ensemble containing both common and innovation components. With a goal of proposing an MMV-type algorithm that is robust to outliers (absence of common sparsity pattern), we propose Greedy Pursuits Assisted Basis Pursuit for Multiple Measurement Vectors (GPABP-MMV). It employs modified basis pursuit and MMV versions of multiple greedy pursuits. We also formulate the exact reconstruction conditions and the reconstruction error bound for GPABP-MMV. GPABP-MMV is suitable for a variety of applications including time-sequence reconstruction of video frames, reconstruction of ECG signals, etc.

An FIR approximation of spectral transformation is proposed that could transform any FIR prototype to another FIR filter with a desired frequency mapping. Examples of several tunable filters including cascaded integrator comb (CIC) and interpolated FIR (IFIR) filters, along with their realizations, are presented using the proposed transformation.

Noise incursion is an inherent problem in dictionary training on noisy samples. Therefore, enforcing a structural constrain on the dictionary will be useful for a stable dictionary training. Recently, a sparse dictionary with predefined sparsity has been proposed as a structural constraint. However, a fixed sparsity can become too rigid to adapt to the training samples. In order to address this issue, this article proposes a better solution through sparse Sequential Generalization of K-means (SGK). The beauty of the sparse-SGK is that it does not enforce a predefined rigid structure on the dictionary. Instead, a flexible sparse structure automatically emerges out of the training samples depending on the amount of noise. In addition, a variation of sparse-SGK using an orthogonal base dictionary is proposed for a quicker training. The advantages of sparse-SGK are demonstrated via 3-D image denoising. The experimental results confirm that sparse-SGK has better denoising performance and it takes lesser training time.

In distributed compressive sensing, if one signal in a joint-sparse signal ensemble is known apriori, the remaining signals can be reconstructed using modified Compressive Sensing (CS) algorithms such as Modified Basis Pursuit (Mod-BP) which makes use of Partially Known Support (PKS). Though Mod-BP reconstructs the joint-sparse signals with high accuracy, it takes a huge amount of time to converge. This might not be desirable in some practical applications like CS reconstruction of video frames. Carrillo et al have illustrated the use of PKS in iterative greedy algorithms to improve the recovery performance at a much shorter time. However, PKS based iterative greedy algorithms are totally blind about the wrong atoms present in the PKS, which is likely for video frames. To overcome this, we propose Adaptive Backtracking Matching Pursuit (AdBMP) which makes effective use of the PKS to reconstruct the sparse signal. Experimental results show that AdBMP gives a better reconstruction accuracy compared to that of the existing PKS based iterative greedy algorithms.

Existing image denoising frameworks via sparse representation using learned dictionaries have an weakness that the dictionary, trained from noisy image, suffers from noise incursion. This paper analyzes this noise incursion, explicitly derives the noise component in the dictionary update step, and provides a simple remedy for a desired signal to noise ratio. The remedy is shown to perform better both in objective and subjective measures for lesser computation, and complements the framework of image denoising.

In Distributed Compressive Sensing (DCS), correlated sparse signals stand for an ensemble of signals characterized by presenting a sparse correlation. If one signal is known apriori, the remaining signals in the ensemble can be reconstructed using l1-minimization with far fewer measurements compared to separate CS reconstruction. Reconstruction of such correlated signals is possible via Modified-CS and Regularized-Modified-BP. However, these methods are greatly influenced by the support set of the known signal that includes locations irrelevant to the target signal. While recovering each signal, prior to Modified-CS or Regularized-Modified-BP, we propose an adaptation step to retain only the sparse locations significant to that signal. We call our proposed methods as Modified-Adaptive-BP and Regularized-Modified-Adaptive-BP. Theoretical guarantees and experimental results show that our proposed methods provide efficient recovery compared to that of the Modified-CS and its regularized version.

Directionlets allow a construction of perfect reconstruction and critically sampled multidirectional anisotropic basis, yet retaining the separable filtering of standard wavelet transform. However, due to the spatially varying filtering and downsampling direction, it is forced to apply spatial segmentation and process each segment independently. Because of this independent processing of the image segments, directionlets suffer from the following two major limitations when applied to, say, image coding. First, failure to exploit the correlation across block boundaries degrades the coding performance and also induces blocking artifacts, thus making it mandatory to use deblocking filter at low bit rates. Second, spatial scalability, i.e., minimum segment size or the number of levels of the transform, is limited due to independent processing of segments. We show that, with simple modifications in the block boundaries, we can overcome these limitations by, what we call, in-phase lifting implementation of directionlets. In the context of directionlets using in-phase lifting, we identify different possible groups of downsampling matrices that would allow the construction of a multilevel transform without forcing independent processing of segments both with and without any modifications in the segment boundary. Experimental results in image coding show objective and subjective improvements when compared with the directionlets applied independently on each image segment. As an application, using both the in-phase lifting implementation of directionlets and the adaptive directional lifting, we have constructed an adaptive directional wavelet transform, which has shown improved image coding performance over these adaptive directional wavelet transforms.

Recent dictionary training algorithms for sparse representation like K-SVD, MOD, and their variation are reminiscent of K-means clustering, and this letter investigates such algorithms from that viewpoint. It shows: though K-SVD is sequential like K-means, it fails to simplify to K-means by destroying the structure in the sparse coefficients. In contrast, MOD can be viewed as a parallel generalization of K-means, which simplifies to K-means without perturbing the sparse coefficients. Keeping memory usage in mind, we propose an alternative to MOD; a sequential generalization of K-means (SGK). While experiments suggest a comparable training performances across the algorithms, complexity analysis shows MOD and SGK to be faster under a dimensionality condition.

This paper is concerned with the problem of robust unbiased H∞filtering for uncertain two-dimensional (2-D) systems described by the Fornasini-Marchesini local state-space second model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The concept of robust unbiased filtering is first introduced into uncertain 2-D systems. A necessary and sufficient condition for the existence of robust unbiased 2-D H∞filters is derived based on the rank condition of the given system matrices. A method is then proposed for the design of robust unbiased H∞filters for uncertain 2-D systems using a linear matrix inequality (LMI) technique. The main advantage of the proposed method is that it can be applied to unstable uncertain 2-D systems while existing robust 2-D H∞filtering approaches only work for robust stable uncertain 2-D systems. An illustrative example is also provided and comparison with existing results is made.

This letter presents a variant of Orthogonal Matching Pursuit (OMP) method, called Backtracking-based Adaptive OMP (BAOMP), for compressive sensing and sparse signal reconstruction. As an extension of the OMP algorithm, the BAOMP method incorporates a simple backtracking technique to detect the previous chosen atoms' reliability and then deletes the unreliable atoms at each iteration. Through this modification, the BAOMP method achieves superior performance while maintaining the low complexity of OMP-type methods. Also, unlike its several predecessors, the BAOMP method does not require the sparsity level to be known a priori. The experiments demonstrate the proposed method's superior performance to that of several other OMP-type andl1optimization methods.

This paper is concerned with the problem of the two-channel 2-D IIR filter bank design. Using a systematic optimization approach, which is solved in terms of an LMI, the 2-D IIR synthesis filters are designed such that the systems are alias free and then optimized to achieve approximate perfect reconstruction.

For a given two-dimensional down-sampling, the alias-free ideal filter bank shapes are not unique. In this work finding such shapes and designing such filter banks is investigated. A schematic way to obtain such ideal filter shapes is suggested. Several examples are considered to show how to obtain interesting ideal filter shapes. While known two-dimensional filter bank design schemes cater to specific shapes, a universal design procedure based on lifting is used in this work to design these filter banks.

In this paper we consider the problem of finding the direction of the content in a given image segment to foster the development of adaptive directional decompositions of images. We propose a mechanism based on a new directional metric that we define as Directional Variance (DirVar), a measure of variance along the discrete lines in the given direction. The simulation results in section III, within the frame work of directionlets, and in the lifting based directional DWT, show that our mechanism is very accurate and reliable in finding the content direction and saves lot of computations.

This paper considers the joint source channel coding using a new class of DFT codes which we refer to as Hermitian symmetric DFT (HSDFT) codes. A new decoding algorithm for decoding of HSDFT codes is presented. With this new decoding algorithm and an appropriate transmission scheme, HSDFT codes are capable of correcting more burst errors than the capacity of any maximum distance separable (MDS) code. Experimental results obtained by transmission of image over binary symmetric channel and Gilbert-Elliot channel are also presented, which show that HSDFT codes perform similar to the existing DFT class of codes on a binary symmetric channel while it performs consistently better (by around 2dB) on a Gilbert-Elliot like channel.

The problem of non-fragile H∞filter design for two-dimensional (2-D) discrete systems in Fornasini-Marchesini model with polytopic uncertainties is considered in this paper. The filters to be designed are assumed to be with additive norm-bounded gain variations. By using the technique of imposing a structural restriction on the slack matrix, we present a simple and yet effective method for designing non-fragile H∞filters. Explicit expressions of the non-fragile H∞filters are given in terms of solutions to a linear matrix inequality (LMI). An illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.

This paper studies the feasibility and investigates various choices in the application of compressive sensing (CS) to object-based surveillance video coding. The residual object error of a video frame is a sparse signal and CS, which aims to represent information of a sparse signal by random measurements, is considered for coding of object error. This work proposes several techniques using two approaches- direct CS and transform-based CS. The techniques are studied and analyzed by varying the different trade-off parameters such as the measurement index, quantization levels etc. Finally we recommend an optimal scheme for a range of bitrates. Experimental results with comparative bitrates-vs-PSNR graphs for the different techniques are presented.

The recently emerged theory of compressive sensing (CS) has a remarkable result that signals having sparse representations in some known basis can be represented (with high probability) by taking a few random projection measurements of the signals. In this paper, we study some CS sparse reconstruction methods and propose a video object error coding method based on CS theory. The proposed system first assumes the moving objects have been segmented from background image and object-based motion compensated from the previous reconstruction frame, and then the resulting object error is encoded by using CS random matrix projection. Finally the coded measurements can be quantized to store or transmit. Experimental results demonstrate the object error blocks can be effectively recovered by using CS sparse reconstruction algorithms. This proposed method would be widely used in the object-based video compression fields.

The field of ldquosmart surveillancerdquo is an upcoming research area with a lot of work published in the last decade. Perfect segmentation of moving humans from security videos is still a challenge because of lighting variations which causes moving cast shadows in the video. In this paper, we propose a novel technique for the computation of ldquoillumination thresholdrdquo using the idea of frame ratio for shadow-less object segmentation. The method uses an adaptive threshold specific to the characteristics of the current video frame being processed and it is found to show an improvement over the previous models of segmentation using hard threshold. Experimental results for a variety of surveillance video are shown and compared with other previous works to validate the robustness of the proposed method.

Compression of encrypted data is possible by using distributed source coding. In this paper, we consider the encryption, followed by lossless compression of gray scale and color images. We propose to apply encryption on the prediction errors instead of directly applying on the images and use distributed source coding for compressing the cipher texts. The simulation results show that by using the proposed technique comparable compression gains, with compression ratios varying from 1.5 to 2.5 can be achieved despite encryption.

In this letter, we revisit the completeness of the lattice factorization for -channel linear phase perfect reconstruction filter banks (LPPRFBs) with equal length and further investigate a more fundamental problem, i.e., the existence of complete lattice factorization by using LPPR propagating blocks of order-one causal FIR with anticausal FIR inverse (CAFACAFI) matrices. Reviewing the previous works, we point out the limitation of the existing LPPR propagating blocks and then show its consequence for incompleteness of the existing lattice factorizations. Furthermore, we show the nonexistence of any order-one LPPR propagating block by using CAFACAFI matrices. In addition, the completeness of lattice factorizations has been re-examined for generalized lapped orthogonal transforms (GenLOTs) and lapped biorthogonal transforms (LBTs) with linear phase based on the analysis developed in this letter.

Visual tracking has been a challenging problem in computer vision over the decades. The applications of Visual Tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. Mean-shift (MS) tracker, which gained more attention recently, is known for tracking objects in a cluttered environment and its low computational complexity. The major problem encountered in histogram-based MS is its inability to track rapidly moving objects. In order to track fast moving objects, we propose a new robust mean-shift tracker that uses both spatial similarity measure and color histogram-based similarity measure. The inability of MS tracker to handle large displacements is circumvented by the spatial similarity-based tracking module, which lacks robustness to object's appearance change. The performance of the proposed tracker is better than the individual trackers for tracking fast-moving objects with better accuracy.

Visual tracking has been a challenging problem in computer vision over the decades. The applications of visual tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. In this paper we present a novel object tracker based on fast learning radial basis function (RBF) networks. Here, the object and background pixel-based color features are used to develop object/non-object RBF classifiers. The posterior probability information of these classifiers are used for developing an efficient object model for tracking in the subsequent frames. The performance of the proposed tracker is tested with many video sequences of real-life complexity and compared against the color-based mean-shift tracker. The proposed tracker is illustrated to be suitable for real-time robust object tracking due to its low computational complexity.

This paper studies the robustness of filter bank (FB) frame in l2(Zopf) to quantization and erasures from the perspective of both frame and FB theory. It is shown that the equal-norm property, imposed frequently in previous papers, is not necessary for optimization of frames under certain conditions and not desirable from the viewpoint of designing FB frames. We introduce a novel notion, named frame energy, which actually dictates the quantization performance of FB frames. Then, the erasure effects on the structures and quantization performance of FB frames are investigated. The design freedom obtained from removing the equal-norm property is explained and illustrated with examples.

Video surveillance is currently one of the most active area of research in both academia and industry. Though much work has been done in the area of smart surveillance, relatively little work has been reported to compress the surveillance videos. In this paper, we propose an object based video compression system using foreground motion compensation for applications such as archival and transmission of surveillance video. The proposed system segments independently moving objects from the video and codes them with respect to the previously reconstructed frame. The error resulting from object-based motion compensation is coded using SA-DCT procedure. The proposed system codes the surveillance video using far lesser bits compared to conventional video compression techniques

Resampling matrices are essential in multidimensional multirate signal processing. However, different resampling matrices may correspond to the same resampling pattern. It is surely more effective to study such distinct patterns rather than study exhaustively all the possible cases, which is infinite. Motivated by this, we study the resampling patterns for a given decimation ratio in this paper. Our analysis enumerates the number of distinct resampling patterns for any prime decimation ratio, and provides an upper bound on the number for any composite decimation ratio. Parametrization of these distinct patterns is also proposed. Among these patterns, patterns which are nonseparable are also enumerated and parameterized separately

This paper introduces the lattice factorizations and designs of a large class of linear phase perfect reconstruction filter banks. We deal with FIR filter banks with real-valued coefficients in which all filters have the same arbitrary length and symmetry center. Existence conditions on the length are given first. Lattice structures are developed for both even and odd channel filter banks. Compared to most existing design methods, the proposed approach can offer better trade off between performance and filter length. Finally, several design and image coding examples are presented to validate our approach.

For multidimensional system, since the factorization theory is not well developed and multivariate system is generally much complex than univariate system, they are much less mature than ID filter banks. In this paper, a class of 2-D 2-channel linear phase perfect reconstruction filter banks is investigated. Based on a proposed conjecture, a lifting based approach to factorize a given FB of this class is presented. Though may not be provably complete, a construction method related to the factorization is also proposed. It is also compared with McClellan transform based design, and found to be better in terms of filter performance.

This paper introduces characterization of over-sampled linear phase perfect reconstruction filter bank as an embedded part of corresponding critically sampled filter bank. We deal with FIR linear phase perfect reconstruction filter banks with real-valued coefficients in which all analysis filters have the same length. Two methods are presented for designing such filter banks with integer oversampling ratio and rational oversampling ratio, respectively. Finally, several design examples are presented to confirm the validity of our approach.

Lifting is advantageous for its structurally perfect reconstruction property of a filter bank. Based on such lifting structure, this paper is focused on factorization of 2-channel linear phase perfect reconstruction filter bank. We propose factorizations that are also structurally linear phase for this kind of filter bank. For different types of filter banks, we use different approaches to achieve it. We apply the factorization to existing filter banks, and illustrate its advantage towards efficient implementation and reduced precision implementation.

When a document or a sequence of characters is tampered, watermarking should be able to not only detect the tampering but also restore it. Towards this goal, self-embedding is used where the watermark is a copy of the sequence itself. Restoration algorithms for substitution attack are proposed for two variants of self-embedding. These algorithms are analyzed to show where they fail and how to avoid these failures. Strategies to cope with deletion/insertion attacks are also mentioned.

Data embedding in sharply-contrasted binary images like text, drawing, signature and cartoon is a challenging issue due to simple pixel statistics in such images. Arbitrary modification to the pixels can be visually perceptible in the process of data embedding. The use of a valid perceptual model is important to minimize the effect of such visual distortion in binary images. In this paper, a novel perceptual model is used to embed significant amount of information such that the original and the marked images before and after data embedding process are perceptually similar. In our model, the distortion that occurs after flipping a pixel is estimated on the curvature-weighted distance difference (CWDD) measure between two contour segments.

A disadvantage of nonorthogonal transforms is the inevitable amplification of the quantization noise during synthesis. A feedback structure can be used to compensate this amplification. We try to generalize the idea of noise feedback to the case of nonorthogonal transforms. We explore the application of nonorthogonal transforms to the coding of quasi-stationary sources for which the KLT is, strictly speaking, not defined. Transforms which maximize the coding gain for the assumed model of the quasi-stationary source are found, which are generally nonorthogonal. The proposed transforms along with the feedback structure are seen to perform better than the average KLT for AR sources and real life speech signals.

In this work, the problem of design of M channel IIR causal stable perfect reconstruction filter banks is addressed, and design approach based on similarity transformation of the state transition matrix is presented. The analysis and synthesis polyphase matrices are constrained to be minimal. The state transition matrix of the synthesis polyphase is obtained by similarity transformation of the analysis state transition matrix. Simulation results are provided.

We propose a block-based conditional motion estimation scheme for video compression. The blocks in a frame are classified as active or inactive based on a threshold and only the active blocks are subjected to motion estimation. The threshold value is decided automatically through an iterative algorithm. The motion vectors of the boundary active blocks are estimated using a subblock matching-based scheme. Unlike existing variable size block-matching algorithms, the proposed motion estimation scheme preserves the basic framework of the conventional block-matching algorithm, such as equal number of motion vectors and one-pass processing. A small amount of side information needs to be transmitted for the boundary blocks to indicate the displacements of the their subblocks. The proposed scheme provides a better tradeoff between the complexity and the rate-distortion performance of the encoder than other existing schemes and better subjective quality of the motion-compensated frames than the conventional motion compensation.

Proposes some variable-dimension block-based fractal image-coding schemes which employ encoding of fixed and variable-dimension range blocks with fixed and variable-dimension domain blocks. The first decision to be made in a variable-dimension fractal coding scheme is in the choice of the type of image partition used for the range blocks. We propose a partition based on a rate-distortion criterion such that the range block sizes and domain block sizes are selected adaptively by the algorithm itself based on the complexity of the image region that is being encoded. Variable domain blocks address the nonuniformity of fractal scaling across the image as manifested by different resampling ratios across the image. Variable range blocks address the nonstationarity of the image. So, this algorithm provides a general framework of variable range, variable domain fractal encoding. All fixed-dimension fractal coding schemes are constrained variation of this generalized version.

In this paper, a four-parameter model for global motion in image sequences is proposed. The model is generalized and can accommodate global object motions besides the motions due to the camera movements. Only the pan and the zoom global motions are considered because of their relatively more frequent occurrences in real video sequences. Besides the traditional least-squares estimation scheme, two more estimation schemes based on the minimization of the motion field bit rate and the global prediction error energy are proposed. Among the three estimation schemes, the iterative least-squares estimation is observed to be the best because of the least computational complexity, accuracy of the estimated parameters, and similar performance as with the other schemes. Four global motion compensation schemes including the existing pixel-based forward compensation are proposed. It is observed that backward compensation schemes perform similarly to the corresponding forward schemes except for having one frame delay degradation. The pixel based forward compensation is observed to have the best performance. A new motion vector coding scheme is proposed which has similar performance as the two-dimensional entropy coding but needs much less computation. Using the proposed coding scheme with the pixel-based forward compensation, we obtain 61.85% savings in motion field bit rate over the conventional motion compensation for the Tennis sequence.

Conventional error diffusion halftoning uses a causal error filter. We propose the iterative error diffusion algorithm by extending the error diffusion to accommodate noncausal error filters. We realize the importance of the phase response of the error filter in the error diffusion halftoning method, and demonstrate it using examples. Iterative error diffusion is able to realize a zero phase error filter. We also trace a drawback of error diffusion to the shape of the error filter, and provide a remedy. The results obtained using a zero phase error filter in the iterative error diffusion algorithm are, in our opinion, superior to the error diffusion halftones.

The halftone quality of an error diffusion halftone depends on the error filter response. Apart form the magnitude response being a low pass, it is desirable to have a zero phase response. We propose the iterative error diffusion halftoning algorithm that allows use of non-causal error filter (such as zero phase error filter). We present simulation results showing that the proposed halftoning scheme is substantially better, specially in retaining the sharpness of the edges and in truthfullness.

A variable dimension vector quantizer (VDVQ) has codewords of unequal dimensions. Here, a trellis-based sequential optimal VDVQ encoding algorithm is proposed. Also, a VDVQ codebook design algorithm based on splitting a node with equal or reduced dimensions is proposed that does not require any codebook parameter to be prespecified unlike known schemes. The VDVQ system is shown to outperform a few known VQ systems for AR(1) sources.

The input-dependent weighted-square-error (IDWSE) distortion, which is computationally simple, is shown to offer subjectively better decoded images than the mean-square-error (MSE) distortion. In the presence of image activity, better edge representation is achieved for low-bit-rate VQ image coding without sacrificing anything. This strategy produces an optimal codebook in the IDWSE sense and is therefore preferable to the equivalent subcodebook method. A simple way to compute the image activity is proposed and shown to be quite effective. Introducing block boundary sensitivity in IDWSE distortion produces a decoded image with less blockiness and better edge representation, while the encoder computation is marginally raised.>