In electroencephalogram (EEG)-based emotion recognition, traditional static univariate models often struggle to capture the complex, scale-free dynamics inherent in multivariate neural signals, which hampers generalization across subjects. To address this, we introduce a novel stochastic framework based on operator multifractional Lévy stable motion (omLsm) and stochastic differential equations (SDE). This framework effectively captures the dynamic scale-free properties of EEG signals and assesses their local cross-scaling characteristics, revealing dynamic fractal connectivity that correlates with various emotional states. The rationale behind our approach lies in the shared scale-free properties and affective cognitive attributes observed across different subjects within the same emotion categories. Local cross-scaling characteristics expose commonalities in the spatio-temporal and spectral domains, facilitating more robust emotion recognition through a multivariate lens. Furthermore, our framework incorporates domain adaptation strategies that enhance model performance across diverse subject populations. Our results indicate significant differences in scale-free connectivity associated with emotional states, reflecting clear advantages over static univariate approaches. Notably, our detection method achieves maximum accuracy of 98.00% for dominance and 98.41% for arousal recognition, respectively, using the DREMER and DEAP datasets and cross-dataset experiments, demonstrates impressive generalization capabilities of the proposed model. This signifies our method's effectiveness for practical applications in emotion recognition.

Optical coherence tomography (OCT) is a non-invasive and effective tool for the imaging of retinal tissue. However, the heavy speckle noise, resulting from multiple scattering of the light waves, obscures important morphological structures and impairs the clinical diagnosis of ocular diseases. In this paper, we propose a novel and powerful model known as tensor ring decomposition-guided dictionary learning (TRGDL) for OCT image denoising, which can simultaneously utilize two useful complementary priors, i.e., three-dimensional low-rank and sparsity priors, under a unified framework. Specifically, to effectively use the strong correlation between nearby OCT frames, we construct the OCT group tensors by extracting cubic patches from OCT images and clustering similar patches. Then, since each created OCT group tensor has a low-rank structure, to exploit spatial, non-local, and its temporal correlations in a balanced way, we enforce the TR decomposition model on each OCT group tensor. Next, to use the beneficial three-dimensional inter-group sparsity, we learn shared dictionaries in both spatial and temporal dimensions from all of the stacked OCT group tensors. Furthermore, we develop an effective algorithm to solve the resulting optimization problem by using two efficient optimization approaches, including proximal alternating minimization and the alternative direction method of multipliers. Finally, extensive experiments on OCT datasets from various imaging devices are conducted to prove the generality and usefulness of the proposed TRGDL model. Experimental simulation results show that the suggested TRGDL model outperforms state-of-the-art approaches for OCT image denoising both qualitatively and quantitatively.

An improved analysis of Optical Coherence Tomography (OCT) images of the retina is of essential importance for the correct diagnosis of retinal abnormalities. Unfortunately, OCT images suffer from noise arising from different sources. In particular, speckle noise caused by the scattering of light waves strongly degrades the quality of OCT image acquisitions. In this paper, we employ a Modified Morphological Component Analysis (MMCA) to provide a new method that separates the image into components that contain different features as texture, piecewise smooth parts, and singularities along curves. Each image component is computed as a sparse representation in a suitable dictionary. To create these dictionaries, we use non-data-adaptive multi-scale ( X -let) transforms which have been shown to be well suitable to extract the special OCT image features. In this way, we reach two goals at once. On the one hand, we achieve strongly improved denoising results by applying adaptive local thresholding techniques separately to each image component. The denoising performance outperforms other state-of-the-art denoising algorithms regarding the PSNR as well as no-reference image quality assessments. On the other hand, we obtain a decomposition of the OCT images in well-interpretable image components that can be exploited for further image processing tasks, such as classification.

Optical Coherence Tomography (OCT) images, as well as a majority of medical images, are imposed to speckle noise while capturing. Since the quality of these images is crucial for detecting any abnormalities, we develop an improved denoising algorithm that is particularly appropriate for OCT images. The essential idea is to combine two non-data-adaptive transform-based denoising methods that are capable to preserve different important structures appearing in OCT images while providing a very good denoising performance. Based on our numerical experiments, the most appropriate non-data-adaptive transforms for denoising and feature extraction are the Discrete Cosine Transform (DCT) (capturing local patterns) and the Dual-Tree Complex Wavelet Transform (DTCWT) (capturing piecewise smooth image features). These two transforms are combined using the Dual Basis Pursuit Denoising (DBPD) algorithm. Further improvement of the denoising procedure is achieved by total variation (TV) regularization and by employing an iterative algorithm based on DBPD.

Abstract Due to the American cancer society, many people with esophageal adenocarcinoma are not survived. The treatment rate can be significant in the early detection of Barrett's esophagus (BE) as a premalignant stage for adenocarcinoma. An important landmark to detect BE is the Z‐line. BE segmentation is already highly dependent upon the operator's knowledge and skill. The main aim of this study is automatic Z‐line extraction using endoscopic images leading to segmentation of the early BE stage. To this end, a computer‐aided detection method exploiting k‐means clustering, image segmentation using the edge detector, and a novel boundary linking algorithm is proposed. For the evaluation, the gold standard is considered the average contours of Z‐lines extracted by the three experts. The proposed method annotated the Z‐line with the accuracy and precision of 0.92 and 0.87, respectively, and the value of the average boundary distance is 5.9 pixels. To the results and visual inspection, the presented method can be used for efficient and robust extraction of the Z‐line at the early BE stage. Furthermore, it can be used in other medical imaging applications with complex boundaries and low contrast in the images, limiting the common automatic boundary detection methods.

Mixture of symmetric$\alpha$-stable (s$\alpha$s) models can be used to model impulsive data with heavy-tailed distribution. Lack of closed-form expression for$\alpha$-stable distributions is a challenge for efficient mixture modeling in current methods. In this letter, we present an analytical approach for novel solution of parameter estimation in s$\alpha$s mixture models which improves the computational efficiency of the existing methods. In addition, by introducing a centro-symmetrization (CS) transform, we generalize the application of proposed method to non-centered skewed data as well. The proposed method employs the logarithmic moments of data in maximization of conditional expectation of log-likelihood and is called EMLM algorithm. The experimental results on the synthetic and real datasets show that EMLM outperforms current baseline models not only in terms of goodness of fit of model, but also by increasing the performance of down-stream applications such as classification.

This paper presents a new approach for reconstruction of disconnected digital lines (DDLs) based on a constrained regularization model which ensures connectivity of the digital lines (DLs) in the discrete image plane. The first step in this approach is to determine the order of given pixels of the DDL. To determine connectivity of pixels, we use the usual 8-neighbor connectivity in discrete images. For any neighboring pixels of the DDL that are not connected, we determine a number of new pixel values that need to be reconstructed between these pixels. Next, the integer-valued x - and y -coordinates of the location of the pixels of the DDLs are segregated into two 1D signal vectors. Then the x - and y -coordinates of the missing pixels of the DDLs are estimated using a new constrained regularization. While the solution of this constrained minimization problem provides real values for the x - and y -coordinates of pixels positions, the imposed constraint ensures connectivity of the resulting DLs in the image plane after transforming the computed values from [Formula: see text] to [Formula: see text]. The proposed regularization approach forces connected lines with small curvature. The experimental results demonstrate that the proposed technique improves DL intersection detection, as well. Moreover, this technique has a high potential to be used as a fast approach in binary image inpainting particularly overcoming the shortcomings of conventional methods which cause destruction of thin objects and blurring in the recovered regions.

Gastroesophageal reflux disease (GERD) is a common digestive disorder with troublesome symptoms that has been affected millions of people worldwide. Multichannel Intraluminal Impedance-pH (MII-pH) monitoring is a recently developed technique, which is currently considered as the gold standard for the diagnosis of GERD. In this paper, we address the problem of characterizing gastroesophageal reflux events in MII signals. A GER detection algorithm has been developed based on the sparse representation of local segments. Two dictionaries are trained using the online dictionary learning approach from the distal impedance data of selected patches of GER and no specific patterns intervals. A classifier is then designed based on thelp-norm of dictionary approximations. Next, a preliminary permutation mask is obtained from the classification results of patches, which is then used in post-processing procedure to investigate the exact timings of GERs at all impedance sites. Our algorithm was tested on 33 MII episodes, resulting a sensitivity of 96.97% and a positive predictive value of 94.12%.

This paper proposes a mixed low-rank approximation and second-order tensor-based total variation (LRSOTTV) approach for the super-resolution and denoising of retinal optical coherence tomography (OCT) images through effective utilization of nonlocal spatial correlations and local smoothness properties. OCT imaging relies on interferometry, which explains why OCT images suffer from a high level of noise. In addition, data subsampling is conducted during OCT A-scan and B-scan acquisition. Therefore, using effective super-resolution algorithms is necessary for reconstructing high-resolution clean OCT images. In this paper, a low-rank regularization approach is proposed for exploiting nonlocal self-similarity prior to OCT image reconstruction. To benefit from the advantages of the redundancy of multi-slice OCT data, we construct a third-order tensor by extracting the nonlocal similar three-dimensional blocks and grouping them by applying the k-nearest-neighbor method. Next, the nuclear norm is used as a regularization term to shrink the singular values of the constructed tensor in the non-local correlation direction. Further, the regularization approaches of the first-order tensor-based total variation (FOTTV) and SOTTV are proposed for better preservation of retinal layers and suppression of artifacts in OCT images. The alternative direction method of multipliers (ADMM) technique is then used to solve the resulting optimization problem. Our experiments show that integrating SOTTV instead of FOTTV into a low-rank approximation model can achieve noticeably improved results. Our experimental results on the denoising and super-resolution of OCT images demonstrate that the proposed model can provide images whose numerical and visual qualities are higher than those obtained by using state-of-the-art methods.

In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s [Formula: see text]) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s [Formula: see text] distribution. We applied fractional Laplacian operator to image and fitted s [Formula: see text] to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s [Formula: see text] distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.

Age‐related Macular Degeneration (AMD) and Diabetic Macular Edema (DME) are the major causes of vision loss in developed countries. Alteration of retinal layer structure and appearance of exudates are the most significant signs of these diseases. In this paper, with the aim of automatic classification of DME, AMD, and normal subjects using Optical Coherence Tomography (OCT) images, a dictionary‐learning based classification is proposed. The two important issues intended in this approach are avoiding retinal layer segmentation and attempting to mimic the authors' understanding based on normal and abnormal region identifications, considering that the signs of diseases appear in a small fraction of B‐Scans. The histogram of oriented gradients feature descriptor was utilized to characterize the distribution of local intensity gradients and edge directions. To capture the structure of extracted features, different dictionary learning‐based classifiers are employed. The dataset consists of 45 subjects: 15 patients with AMD, 15 patients with DME, and 15 normal subjects. The proposed classifier leads to an accuracy of 95.13, 100.00, and 100.00% for DME, AMD, and normal OCT images, respectively, only by considering 4% of all B‐Scans of a volume, which outperforms the state‐of‐the‐art methods.

In this paper, a multivariate statistical model that is suitable for describing Optical Coherence Tomography (OCT) images is introduced. The proposed model is comprised of a multivariate Gaussianization function in sparse domain. Such an approach has two advantages, i.e. 1) finding a function that can effectively transform the input - which is often not Gaussian - into normally distributed samples enables the reliable application of methods that assume Gaussianity, 2) although multivariate Gaussianization in spatial domain is a complicated task and rarely results in closed-form analytical model, by transferring data to sparse domain, our approach facilitates multivariate statistical modeling of OCT images. To this end, a proper multivariate probability density function (pdf) which considers all three properties of OCT images in sparse domains (i.e. compression, clustering, and persistence properties) is designed and the proposed sparse domain Gaussianization framework is established. Using this multivariate model, we show that the OCT images often follow a 2-component multivariate Laplace mixture model in the sparse domain. To evaluate the performance of the proposed model, it is employed for OCT image denoising in a Bayesian framework. Visual and numerical comparison with previous prominent methods reveals that our method improves the overall contrast of the image, preserves edges, suppresses background noise to a desirable amount, but is less capable of maintaining tissue texture. As a result, this method is suitable for applications where edge preservation is crucial, and a clean noiseless image is desired.

In this paper, a new statistical model is proposed for the single image super-resolution of retinal Optical Coherence Tomography (OCT) images. OCT imaging relies on interfero-metry, which explains why OCT images suffer from a high level of noise. Moreover, data subsampling is carried out during the acquisition of OCT A-scans and B-scans. So, it is necessary to utilize effective super-resolution algorithms to reconstruct high-resolution clean OCT images. In this paper, a nonlocal sparse model-based Bayesian framework is proposed for OCT restoration. For this reason, by characterizing nonlocal patches with similar structures, known as a group, the sparse coefficients of each group of OCT images are modeled by the scale mixture models. In this base, the coefficient vector is decomposed into the point-wise product of a random vector and a positive scaling variable. Estimation of the sparse coefficients depends on the proposed distribution for the random vector and scaling variable where the Laplacian random vector and Generalized Extreme-Value (GEV) scale parameter (Laplacian+GEV model) show the best goodness of fit for each group of OCT images. Finally, a new OCT super-resolution method based on this new scale mixture model is introduced, where the maximum a posterior estimation of both sparse coefficients and scaling variables are calculated efficiently by applying an alternating minimization method. Our experimental results prove that the proposed OCT super-resolution method based on the Laplacian+GEV model outperforms other competing methods in terms of both subjective and objective visual qualities.

The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The proposed methodology in this article is designed to provide 3D Radon space in linogram fashion to facilitate the use of FIRM with cone beam projections (CBP) for the reconstruction of 3D images in a sparse view angles Cone Beam CT (CBCT). For this reason, in the first phase, the 3D Radon space is generated using CBP data after discretization and optimization of the famous Grangeat's formula. The method used in this process involves fast Pseudo Polar Fourier transform (PPFT) based on 2D and 3D Discrete Radon Transformation (DRT) algorithms with no wraparound effects. In the second phase, we describe reconstruction of the objects with available Radon values, using direct inverse of 3D PPFT. The method presented in this section eliminates noises caused by interpolation from polar to Cartesian space and exhibits no thorn, V-shaped and wrinkle artifacts. This method reduces the complexity to for images of size n × n × n The Cone to Radon conversion (Cone2Radon) Toolbox in the first phase and MATLAB/ Python toolbox in the second phase were tested on three digital phantoms and experiments demonstrate fast and accurate cone beam image reconstruction due to proposed.

In this paper a new statistical multivariate model for retinal Optical Coherence Tomography (OCT) B-scans is proposed. Due to the layered structure of OCT images, there is a horizontal dependency between adjacent pixels at specific distances, which led us to propose a more accurate multivariate statistical model to be employed in OCT processing applications such as denoising. Due to the asymmetric form of the probability density function (pdf) in each retinal layer, a generalized version of multivariate Gaussian Scale Mixture (GSM) model, which we refer to as GM-GSM model, is proposed for each retinal layer. In this model, the pixel intensities in each retinal layer are modeled with an asymmetric Bessel K Form (BKF) distribution as a specific form of the GM-GSM model. Then, by combining some layers together, a mixture of GM-GSM model with eight components is proposed. The proposed model is then easily converted to a multivariate Gaussian Mixture model (GMM) to be employed in the spatially constrained GMM denoising algorithm. The Q-Q plot is utilized to evaluate goodness of fit of each component of the final mixture model. The improvement in the noise reduction results based on the GM-GSM model, indicates that the proposed statistical model describes the OCT data more accurately than other competing methods that do not consider spatial dependencies between neighboring pixels.

Localisation of an active capsule endoscope inside the stomach has different challenges. One of them is the estimation of the capsule's roll angle. Another challenge is adjusting the distance between the capsule and the stomach to achieve high‐quality imaging in the region of interest. In this study, an optimised image‐guided localisation (O‐Localisation) method is proposed to estimate the roll angle and the scale factor between the consecutive frames. The distance between the capsule and walls of the stomach can be adjusted using the suggested fuzzy adjuster, which is developed based on the estimated scale factors and calibration parameters. This new method is only based on visual information extracted from wireless capsule endoscope video frames. The results show that this method can accurately estimate the rotation angles and scale factors with errors <0.2% for the angles up to 90° and 0.3% for the scales up to 5, respectively. The method is robust to the brightness changes up to 80% with a maximum error of 0.3%. The computational time is about 1 s and can be considered near real‐time for this application. Accordingly, the O‐Localisation method as a real‐time, robust and precise method for capsule localisation can provide a more efficient controllable and steerable capsule endoscopes.

Optical coherence tomography (OCT) enables instant and direct imaging of morphological retinal tissue and has become an essential imaging modality for ophthalmology diagnosis. As one of the important morphological retinal characteristics, the structural information of retinal layers provides meaningful diagnostic information and is closely related to several retinal diseases. In this letter, we propose a novel layer guided convolutional neural network (LGCNN) to identify normal retina and three common types of macular pathologies, namely, diabetic macular edema, drusen, and choroidal neovascularization. Specifically, an efficient segmentation network is first employed to generate the retinal layer segmentation maps, which can delineate two lesion-related retinal layers associated with the meaningful retinal lesions. Then, two well-designed subnetworks in LGCNN are utilized to integrate the information of two lesion-related layers. Consequently, LGCNN can efficiently focus on the meaningful lesion-related layer regions to improve OCT classification. The experimental results conducted on two clinically acquired datasets demonstrate the effectiveness of the proposed method.

Automatic and accurate classification of retinal optical coherence tomography (OCT) images is essential to assist ophthalmologist in the diagnosis and grading of macular diseases. Clinically, ophthalmologists usually diagnose macular diseases according to the structures of macular lesions, whose morphologies, size, and numbers are important criteria. In this paper, we propose a novel lesion-aware convolutional neural network (LACNN) method for retinal OCT image classification, in which retinal lesions within OCT images are utilized to guide the CNN to achieve more accurate classification. The LACNN simulates the ophthalmologists' diagnosis that focuses on local lesion-related regions when analyzing the OCT image. Specifically, we first design a lesion detection network to generate a soft attention map from the whole OCT image. The attention map is then incorporated into a classification network to weight the contributions of local convolutional representations. Guided by the lesion attention map, the classification network can utilize the information from local lesion-related regions to further accelerate the network training process and improve the OCT classification. Our experimental results on two clinically acquired OCT datasets demonstrate the effectiveness and efficiency of the proposed LACNN method for retinal OCT image classification.

Optical coherence tomography (OCT) is a powerful method for imaging the retinal layers. In this paper, we develop a novel 3D fully convolutional deep architecture for automated segmentation of retinal layers in OCT scans. This model extracts features from both the spatial and the inter-frame dimensions by performing 3D convolutions, thereby capturing the information encoded in multiple adjacent frames. The proposed network is based on an encoder-decoder framework in which the convolution layers are interlaced with pooling layers in the encoder and with unpooling layers in the decoder, respectively. Consequently, a hierarchy of shrinking 3D feature maps are learned in the encoder and enlarged to the size of original input image for semantic segmentation in the decoder. The framework is validated on thirteen 3D OCTs captured by the Topcon 3D OCT with comparisons against two state-of-the-art segmentation methods including one recent 2D deep learning based approach to substantiate its effectiveness.

Estimation of missing digital information is mostly addressed by one or two-dimensional signal processing methods; however, this problem can emerge in multi-dimensional data including 3D images. Examples of 3D images dealing with missing edge information are often found using dental micro-CT, where the natural contours of dental enamel and dentine are partially dissolved or lost by caries. In this paper, we present a novel sequential approach to estimate the missing surface of an object. First, an initial correct contour is determined interactively or automatically, for the starting slice. This contour information defines the local search area and provides the overall estimation pattern for the edge candidates in the next slice. The search for edge candidates in the next slice is performed in the perpendicular direction to the obtained initial edge in order to find and label the corrupted edge candidates. Subsequently, the location information of both initial and nominated edge candidates are transformed and segregated into two independent signals (X-coordinates and Y-coordinates) and the problem is changed into error concealment. In the next step, the missing samples of these signals are estimated using a modified Tikhonov regularization model with two new terms. One term contributes in the denoising of the corrupted signal by defining an estimation model for a group of mildly destructed samples, and the other term contributes in the estimation of the missing samples with the highest similarity to the samples of the obtained signals from the previous slice. Finally, the reconstructed signals are transformed inversely to edge pixel representation. The estimated edges in each slice are considered as initial edge information for the next slice and this procedure is repeated slice by slice until the entire contour of the destructed surface is estimated. The visual results as well as quantitative results (using both contour-based and area-based metrics) for seven image datasets of tooth samples with considerable destruction of the dentin-enamel junction (DEJ) demonstrates that the proposed method can accurately interpolate the shape and the position of the missing surfaces in computed tomography images in both two and three dimensions (e.g. 14.87 ±3.87 μ m of mean distance (MD) error for the proposed method versus 7.33 ±0.27 μm of MD error between human experts and 1.25 ±~0 % error rate (ER) of the proposed method versus 0.64 ±~0 % of ER between human experts (~1% difference)).

Computer-aided diagnosis (CAD) of retinal pathologies is a current active area in medical image analysis. Due to the increasing use of retinal optical coherence tomography (OCT) imaging technique, a CAD system in retinal OCT is essential to assist ophthalmologist in the early detection of ocular diseases and treatment monitoring. This paper presents a novel CAD system based on a multi-scale convolutional mixture of expert (MCME) ensemble model to identify normal retina, and two common types of macular pathologies, namely, dry age-related macular degeneration, and diabetic macular edema. The proposed MCME modular model is a data-driven neural structure, which employs a new cost function for discriminative and fast learning of image features by applying convolutional neural networks on multiple-scale sub-images. MCME maximizes the likelihood function of the training data set and ground truth by considering a mixture model, which tries also to model the joint interaction between individual experts by using a correlated multivariate component for each expert module instead of only modeling the marginal distributions by independent Gaussian components. Two different macular OCT data sets from Heidelberg devices were considered for the evaluation of the method, i.e., a local data set of OCT images of 148 subjects and a public data set of 45 OCT acquisitions. For comparison purpose, we performed a wide range of classification measures to compare the results with the best configurations of the MCME method. With the MCME model of four scale-dependent experts, the precision rate of 98.86%, and the area under the receiver operating characteristic curve (AUC) of 0.9985 were obtained on average.

Symmetry analysis of right and left eyes can be a useful tool for early detection of eye diseases. In this study, we want to compare the Optical Coherent Tomography (OCT) images captured from optic nerve head (ONH) of right and left eyes. To do this, it is necessary to align the OCT data and compare equivalent B-scans in right and left eyes. For this reason, since the fovea-ONH axes in OCT data are not available due to small field of view in OCT, at first the projection of OCT data of each eye is registered to its corresponding fundus image using extracted vessels by Hessian analysis of directional curvelet subbands. Then, by alignment of fundus images of right and left eyes according to their automatically detected fovea-ONH axes, OCT projections are also aligned. After alignment of OCT projections, aligned B-scans are estimated and used for comparing different parameters such as cup-to-disk ratio (CDR). Using aligned B-scans, two signals of CDRs are obtained from two eyes which each point in these signals corresponds to CDR in a specific part of ONH, i.e., a point-to-point comparison between CDRs of right and left eyes is provided which has potential to lead to a new imaging biomarker for eye disease detection.

Optic Disc (OD) detection in retinal fundus images is a crucial stage for the automation of a screening system in diabetic ophthalmology. Most researches for automatic localization of OD benefit the regions of vessels. In this paper, we present a fast and novel method based on the Circlet Transform to detect OD in digital retinal fundus images that doesn't utilize the location of the vessels. First, each R, G and B band is enhanced using CLAHE method. Then, the enhanced image in RGB color space is converted to L*a*b one. Next, the Circlet transform is applied to the L* band, and finally, the Circlet transform coefficients are analyzed to find the location of the OD. The proposed algorithm is implemented on DRIVE dataset and the experimental results show a very well OD localization. The correct rate of the proposed method is 95% even though it doesn't utilize the vessels' structure.

In this paper, a new model for retinal Optical Coherence Tomography (OCT) images is proposed. This statistical model is based on introducing a nonlinear Gaussianization transform to convert the probability distribution function (pdf) of each OCT intra-retinal layer to a Gaussian distribution. The retina is a layered structure and in OCT each of these layers has a specific pdf which is corrupted by speckle noise, therefore a mixture model for statistical modeling of OCT images is proposed. A Normal-Laplace distribution, which is a convolution of a Laplace pdf and Gaussian noise, is proposed as the distribution of each component of this model. The reason for choosing Laplace pdf is the monotonically decaying behavior of OCT intensities in each layer for healthy cases. After fitting a mixture model to the data, each component is gaussianized and all of them are combined by Averaged Maximum A Posterior (AMAP) method. To demonstrate the ability of this method, a new contrast enhancement method based on this statistical model is proposed and tested on thirteen healthy 3D OCTs taken by the Topcon 3D OCT and five 3D OCTs from Age-related Macular Degeneration (AMD) patients, taken by Zeiss Cirrus HD-OCT. Comparing the results with two contending techniques, the prominence of the proposed method is demonstrated both visually and numerically. Furthermore, to prove the efficacy of the proposed method for a more direct and specific purpose, an improvement in the segmentation of intra-retinal layers using the proposed contrast enhancement method as a preprocessing step, is demonstrated.

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image interpolation method outperforms previous state-of-the-art methods with an acceptable bound.

Asymmetry analysis is a challenging step in computerized early diagnosis of Diabetic retinopathy (DR) which provides an opportunity for early treatment. In this study to compare the patterns of vascular in right and left eyes, a combination of fractal analysis and radon transformation is investigated to provide both statistical distribution of the vessel thickness, and their geometrical distribution. For this purpose, the vessel segmentation and skeletonizetion are performed and the vessels' thickness map (VTM) is obtained. Then, the fractal dimension (FD) is found on various versions like the segmented vessels, skeletonized vessels, VTM, and radon transform (RT) of VTM in right and left eyes for asymmetry analysis. According to the obtained results for mean/SD values of the differences of FDs in right and left eyes and p-values, we conclude that RT of VTM is able to better discriminate two eyes from each other and accordingly, it can be used as a powerful feature for comparison of the symmetry/asymmetry in fundus images. Our evaluation results show that a difference of 0.33 ± 0.11 between FD of VTM's RT in left and right eyes is expected for normal subjects.

Leukemia (a cancer of leukocytes) basically develops in the bone marrow. Acute myelogenous leukemia (a type of leukemia) has eight sub-types according to French-American-British classification. These forms can be visually observed by pathologists using microscopic images of infected cells. However, identification task is tedious and usually difficult due to varying features. Automatic leukemia detection is an important topic in the domain of cancer diagnosis. This paper presents a novel method based on dictionary learning and sparse representation for detecting and classification of different sub-types of AML. For each class, two intensity and label dictionaries are designed for representation using image patches of training samples. New image is represented by all dictionaries and the one with minimum error determine the type of class. We considered M2, M3 and M5 sub-types for evaluation of the method. The initial implementing of the proposed method achieved 97.53% average accuracy for different sub-types of AML.

In this experiment, a gene selection technique was proposed to select a robust gene signature from microarray data for prediction of breast cancer recurrence. In this regard, a hybrid scoring criterion was designed as linear combinations of the scores that were determined in the mutual information (MI) domain and protein-protein interactions network. Whereas, the MI-based score represents the complementary information between the selected genes for outcome prediction; and the number of connections in the PPI network between the selected genes builds the PPI-based score. All genes were scored by using the proposed function in a hybrid forward-backward gene-set selection process to select the optimum biomarker-set from the gene expression microarray data. The accuracy and stability of the finally selected biomarkers were evaluated by using five-fold cross-validation (CV) to classify available data on breast cancer patients into two cohorts of poor and good prognosis. The results showed an appealing improvement in the cross-dataset accuracy in comparison with similar studies whenever we applied a primary signature, which was selected from one dataset, to predict survival in other independent datasets. Moreover, the proposed method demonstrated 58-92 percent overlap between 50-genes signatures, which were selected from seven independent datasets individually.

In this paper, we address the problem of recovering degraded images using multivariate Gaussian mixture model (GMM) as a prior. The GMM framework in our method for image restoration is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering. Our conducted experiments show that in the case of constraining Gaussian estimates into a finite-sized windows, the patch clusters are more likely to be derived from the estimated multivariate Gaussian distributions, i.e., the proposed statistical patch-based model provides a better goodness-of-fit to statistical properties of natural images. A novel approach for computing aggregation weights for image reconstruction from recovered patches is introduced which is based on similarity degree of each patch to the estimated Gaussian clusters. The results admit that in the case of image denoising, our method is highly comparable with the state-of-the-art methods, and our image interpolation method outperforms previous state-of-the-art methods.

In this paper, we discuss about applications of different methods for decomposing a signal over elementary waveforms chosen in a family called a dictionary (atomic representations) in optical coherence tomography (OCT). If the representation is learned from the data, a nonparametric dictionary is defined with three fundamental properties of being data-driven, applicability on 3D, and working in multi-scale, which make it appropriate for processing of OCT images. We discuss about application of such representations including complex wavelet based K-SVD, and diffusion wavelets on OCT data. We introduce complex wavelet based K-SVD to take advantage of adaptability in dictionary learning methods to improve the performance of simple dual tree complex wavelets in speckle reduction of OCT datasets in 2D and 3D. The algorithm is evaluated on 144 randomly selected slices from twelve 3D OCTs taken by Topcon 3D OCT-1000 and Cirrus Zeiss Meditec. Improvement of contrast to noise ratio (CNR) (from 0.9 to 11.91 and from 3.09 to 88.9, respectively) is achieved. Furthermore, two approaches are proposed for image segmentation using diffusion. The first method is designing a competition between extended basis functions at each level and the second approach is defining a new distance for each level and clustering based on such distances. A combined algorithm, based on these two methods is then proposed for segmentation of retinal OCTs, which is able to localize 12 boundaries with unsigned border positioning error of 9.22 ±3.05 μm, on a test set of 20 slices selected from 13 3D OCTs.

We introduce a nonparametric approach to multiscale segmentation of images using a hierarchical matrix analysis framework called diffusion wavelets. This approach benefits from the advantages of both graph theory and wavelet transform. Till now a broad range of multiscale transforms like wavelets (and other x-lets) have been introduced for image segmentation task. The graph theoretic formulation of grouping is also well-known to deal with this problem. The combination of multiscale transforms and graph based partitioning results in a scale-spectral method exploring through different scales of the image, over a great deal of spectral methods in graph partitioning. The method constructs multiscale basis functions and a series of dilation and orthogonalizations build a hierarchy, automatically. At each level, a set of basis functions is built by applying dyadic powers of a diffusion operator on the bases at the lower level. Two approaches are proposed for multiscale segmentation of images using diffusion wavelets. The first method is based on extended bases functions at each level and designing a competition between the bases value for partitioning. The second approach is defining a new distance for each level and clustering based on such distances.

Microarray technology has become a power tool in the field of bioinformatics. It is used to measure gene expression levels and similar to any other image capturing processes is prone to noise. There are different kinds of noise, during preparation, hybridization and scanning in microarray images which usually are modeled by Gaussian noise. Since introduction of wavelets in 1970s, many more forms and extensions of this transform have been developed and used, such as stationary wavelet transform (SWT), complex wavelet transform (CWT), curvelet transform (CURV) and contourlet transform (CNT). By developing of more sparse transforms, it is important to have a perspective of how efficient the transforms are in different applications, such as microarray image analysis. In this paper, we compare the efficiency of common sparse transforms including ordinary discrete wavelet transform (DWT), SWT, CWT, CURV, CNT, Contourlet-SD decomposition, steerable pyramid (STP) and shearlet transform (SHR) for microarray image denoising. Therefore after converting microarray image into x-let transform, BayesShrink method, soft and hard thresholding are used to perform denoising of these images. Both local and general thresholds are calculated for each subband in order to evaluate the effect of incorporating intrascale dependency on top of sparsity property in statistical modeling of x-let's coefficients. Our simulation results show that CWT and SHR outperforms the others when using global thresholding and SWT is the preferred transform when using local thresholding. Although STP and SHR have better performance for some criteria like structural similarity (SSIM) index, but CWT is faster.

The correct segmentation of blood vessels in optical coherence tomography (OCT) images is an important requirement for better diagnosis of many retinal diseases. Although OCT blood vessel segmentation is often performed by applying vessel detection methods on 2D projection of OCT datasets, some papers investigate the vessel segmentation on OCT slices. The presence of shadows in outer retinal layers is established as the main factor for vessel localization; however, the shadow information fails to localize many important blood vessels. The proposed method is based on anatomical changes of Retinal Nerve Fiber Layer (RNFL) in presence of vessels. In this paper we find the thickening of RNFL by applying a layer segmentation algorithm on OCT slices and combine this information with shadow localization. Furthermore, a vessel detection method based on curvelet transform is also applied on 2D projection of OCTs to be added to localized vessels from OCTs. The results show that combination of vessel detection on 2D projection with vessel localization on OCTs can improve the accuracy up to 0.96 which is promisingly higher than older methods.

Optical coherence tomography (OCT) is known to be one of the powerful and noninvasive methods in retinal imaging. OCT uses retroreflected light to provide micron-resolution, cross-sectional scans of biological tissues. In contrast to OCT technology development, which has been a field of active research since 1991, OCT image segmentation has only been fully explored during the last decade. In this paper, we introduce a fast segmentation method based on a new kind of spectral graph theory named diffusion maps. The research is performed on spectral domain OCT images depicting normal macular appearance. In contrast to our recent methods of graph based OCT image segmentation, the presented approach does not require edge-based image information and rather relies on regional image texture. Consequently, the proposed method demonstrates robustness in situations of low image contrast or poor layer-to-layer image gradients. This method is tested on thirteen 3D macular SD-OCT images obtained from eyes without pathologies with Topcon 3D OCT-1000 imaging system (with a size of 650 × 512 × 128 voxels and a voxel resolution of 4.81 × 13.67 × 24.41 μm3). The mean unsigned and signed border positioning errors (mean ± SD) was 8.52±3.13 and -4.61±3.35 micrometers, respectively. The average computation time of the proposed algorithms (implemented with MATLAB) was 12 seconds per 2D slice.

This paper presents a novel algorithm for automatic extraction of the blood vessels centerline in Fundus Fluorescein Angiography (FFA) images in different diabetic retinopathy (DR) stages. First, the background normalized images are enhanced by applying a morphological edge detector. Then each of the directional images resulting from curvelet sub-bands is individually processed using Hessian matrix and first order derivative of the directional images information in a multi-scale framework for extracting initial centerline segments. Every resulted candidate segment in previous step is confirmed or rejected based on the length and intensity features and eigenvalues analysis. The final vessels centerline segmentation is obtained by connecting the images subsets in a binary image. The proposed algorithm is tested on 70 FFA images from different DR stages and the performance of method in terms of true positive ratio (TPR) and false positive ratio (FPR) that are obtained .9017 and .0983 respectively.

The new techniques of three‐dimensional (3D)‐optical coherence tomography (OCT) imaging is very useful for detecting retinal pathologic changes in various diseases and determining retinal thickness ‘abnormalities’. Fundus colour images have been used for several years for detecting retinal abnormalities too. If the two image modalities were combined, the resulted image would be more informative. The first step to combine these two modalities is to register colour fundus images with an en face representation of OCT. In this study, curvelet transform is used to extract vessels for both modalities. Then the extracted vessels from two modalities are registered together in two stages. At first, images are registered using scaling and translation transformations. Then a quadratic transformation model is assumed between two pairs of images; because retina is imaged as a second‐order surface. Twenty‐two eyes (17 macular and 5 prepapillary), from random patients, were imaged in this study with Topcon 3D OCT1000 instrument. A new registration error is defined which averages the distance between all the corresponding points in two sets of vessels. Results show that registration error after stage one is 6.01 ± 1.82 pixels and after stage two is 1.02 ± 0.02 pixels.

The ability to transform orthogonal 3-lead Vector-cardiogram (VCG) to 12-lead Electrocardiogram (ECG) enables the use of fewer leads for computer visualization, signal analysis and wireless transmission of signals. This can also improve mobility, albeit limited, to the patients. We presented a least square (LS)-based approach to transform 3-lead Frank VCG to 12-lead ECG signals and vice versa, using partial linear transformation. Also our partial linear transformation function would be compared with Dower and affine transformation functions. The VCG and ECG signals of 40 healthy persons are acquired in this study. The results show that for healthy subjects, our partial linear LS method that is maps 3-lead VCG to12-lead ECG more accurately than both Dower and affine transformations of the ECG recordings.

Various techniques are used in diagnosing cardiac diseases. One of these techniques is using electrocardiogram (ECG) tool. In special cardiac cases like atrial fibrillation and posterior myocardial infraction the cardiologist need some information from posterior side of the patient heart, that it can be achieved by using right-posterior ECG method (17 lead ECG). In right-posterior method, position of the patient must be changed in his/her side, so time is waste and patient would be more tired because of taking ECG signals two times. In this study vectorcardiogram (VCG) signals are used as a tool for providing posterior information of the heart. However because for cardiologists is much easier to work with ECG signals for detecting some cardiac diseases, in this study a new method using partial linear transformation is introduced to get posterior ECG leads (V7, V8, V9) from VCG signal. VCG and ECG signals that were used in this study obtained from 30 healthy persons. We presented a statistical approach to transform 3-lead Frank VCG to 15-lead ECG signals and vice versa, based on partial linear transformation (Least Square Method). Also our linear transformation function would be compared with affine transformation functions. The recorder device was Cardiax digital recorder system. The results show that for healthy subjects, the partial linear transformation (least square method) that is presented in this paper maps 3-lead VCG to15-lead ECG, is more accurate than affine transformation function. Regarding the obtained results in this study, ECG signals that derived from VCG signals by using our method was more similar to measured ECG signals than ones derived by using affine transformation. Therefore, by using this transformation function achieving to posterior information of the case heart would be more accurate and useful.

In recent years, advanced analysis of retinal images, has built automatic systems for diagnosis of various diseases. These devices help us save both time and money. The new techniques of 3D-Optical Coherence Tomography (OCT) imaging is very useful for detecting retinal pathologic changes in various diseases and determining retinal thickness abnormalities. Fundus color images have been used for several years for detecting retinal abnormalities too. If the two image modalities were combined, the resulted image would be more informative because some abnormalities such as drusen, geographic atrophy, and macular hemorrhages are detected in color fundus images but the exact morphology and localization of these abnormalities are released in OCT images. The first step to combine the different modalities is to register color fundus images with OCT projection. Ten eyes were imaged in this study with Topcon 3D OCT-1000 instrument. This instrument is used to observe the retina, take fundus and tomograms and record them. An en face representation of OCT reflectivity can be registered with color fundus photography. In this study curvelet transform is used to extract vessels for both modalities. Then the extracted vessels from two modalities are registered together. In this way more blood vessels can be obtained and the results would be more informative.

In this paper we investigate the local probability density function (pdf) of natural signals in sparse domains. The statistical properties of natural signals are characterized more accurately in the sparse domains because the sparse domain coefficients (SDCs) have heavy-tailed distribution and have reduced correlation with adjacent coefficients. Our experiments show that a conditionally (given locally estimated variance and shape) independent Bessel K-form (BKF) pdf locally fits the sparse domain's coefficients of natural signals, accurately. To justify this observation, we also investigate the pdf of the locally estimated variance and suggest a Gamma pdf for the locally estimated variance. Since commonly used sparse transformations are orthonormal, the pdf of the sparse domain coefficients must converge to Gaussian distribution by virtue of central limit theorem assuming that natural signals are locally wide sense stationary for small window sizes. Interestingly, we observe that the pdf of the normalized data (on the locally estimated variance) exhibit a Gaussian pdf, which justifies why the BKF pdf is an appropriate fit.

Red lesions in the form of Microaneurysms (MAs) and Hemorrhages (HMs) are among the first explicit signs of diabetic retinopathy (DR). Hence robust detection of these lesions is an important diagnostic task in computer assistance systems. In this paper we present a new curvelet based algorithm to separate these red lesions from the rest of the color retinal image. In order to prevent fovea to be considered as red lesion, we introduce a new illumination equalization algorithm and apply that to green plane of retinal image. In the next stage, we apply digital curvelet transform (DCUT) to produced enhanced image and modify curvelet coefficients in order to lead red objects to zero. Then we separate these lesions as candidate region by applying an appropriate threshold. Finally, the total structure of blood vessel is extracted employing a curvelet-based technique and the false positives (FPs) are eliminated by subtracting the vessel structure from the candidate images. Experiments on 89 retinal images of diabetic patients indicate that we are able to achieve 94% sensitivity and 87% specificity in detection of red lesion.

This paper presents a new algorithm for video deblurring using frames before and after each scene as a multiframe observation from that scene. For this reason we develop the recently proposed algorithms that try to benefit from advantages of advanced denoising methods. At first the data is transformed to discrete complex wavelet transform (DCWT) and an initial estimate of clean data and point spread function (PSF) is obtained based on minimization of the energy criterion in gradient projection algorithm. In the next stage we improve the estimated clean data using a denoising method employing local Laplace prior and the estimated PSF is enhanced using an anisotropic spatially adaptive denoising procedure based on the local polynomial approximation (LPA) of blur operator and the intersection of confidence intervals (ICI) used for selection of window sizes of LPA. The mentioned procedure is repeated (in gradient projection algorithm) to obtain the appropriate estimations of PSF and clean data. Applying this technique for deblurring of video sequences produces better results in comparison with other methods.

In the recent years, denoising based on the spatially adaptive algorithms that employ anisotropic adaption have been developed. These methods are able to match to the local statistics, preserve the edges and truly remove the noise from the texture of the images. On the other hand, a huge proportion of image enhancement methods are implemented in the sparse domains (e.g., wavelets, curvelets, contourlets and steerable pyramid decomposition) due to impressive properties of these transforms such as heavy-tailed nature of marginal distribution, locality and multiresolution. In this paper we try to establish a relation between two mentioned approaches by estimating the local variances of steerable pyramid coefficients using a shape-adaptive window.

This paper presents an efficient method for automatic extraction of blood vessels in retinal images to improve the detection of low contrast and narrow vessels. The proposed algorithm is composed of four steps: curvelet-based contrast enhancement, match filtering, curvelet-based edge extraction, and length filtering. In this base, after reconstruction of enhanced image from the modified curvelet coefficients, match filtering is used to intensify the blood vessels. Then we employ curvelet transform to segment vessels from its background and finally the length filtering is used to remove the misclassified pixels. The performance of algorithm is evaluated on DRIVE [1] databases and compared with those obtained from a hand-labeled ground truth. Since the curvelet transform is well-suited to handle curve discontinuities, we achieve an area under ROC curve of 0.9631 that demonstrates improved performance of proposed algorithm compared with known techniques.

In this paper, we present a new image denoising algorithm. We assume a mixture of bivariate circular symmetric Laplacian probability density functions (pdfs) where for each wavelet coefficients may have different local parameter. This pdf characterizes simultaneously 1) the heavy-tailed nature, 2) the interscale dependencies of the wavelet coefficients and also 3) the empirically observed correlation between the coefficient amplitudes. We employ this local bivariate mixture model to derive a Bayesian image denoising technique. This proposed pdf, potentially can fits better the statistical properties of the wavelet coefficients than several other existing models. Our simulation results reveal that the proposed denoising method is among the best reported in the literature. This is justified since the accuracy of the employed distribution for noise-free data determines the denoising performance.

The performance of various estimators, such as maximum a posteriori (MAP) is strongly dependent on correctness of the proposed model for noise-free data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is very important in the wavelet based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with a mixture of Laplace probability density functions (pdfs) that uses local parameters for the mixture model. The mixture model is able to capture the heavy-tailed nature of wavelet coefficients and the local parameters can model the empirically observed correlation between the coefficient amplitudes. Therefore, by using this relatively new model, we are able to model the statistical properties of wavelet coefficients. Within this framework, we describe a novel method for image denoising based on designing a MAP estimator, which relies on the mixture distributions with high local correlation. The simulation results show that our proposed technique achieves better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR).

Recently, it has been shown that algorithms exploiting dependencies between coefficients for modeling probability density function (pdf) of wavelet coefficients, could achieve better results for image denoising in wavelet domain compared with the ones based on the independence assumption. In this context, we design a bivariate maximum a posteriori (MAP) estimator which relies on a mixture of bivariate Laplacian models. This model not only is bivariate but also is mixture and therefore, using this new statistical model, we are able to better capture heavy-tailed natures of the data as well as the interscale dependencies of wavelet coefficients. The simulation results show that our proposed technique achieves better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR)