Retinal vessel inpainting using recursive least square dictionary learning algorithm

This work presents a video compression method based on sparse representation and dictionary learning algorithms. The proposed scheme achieves superb rate-distortion performance and decent subjective quality, compared to modern standards, especially at low bit-rates. Different from similar works, sparse representation is employed here for both intra-frame and block matching inter-frame motion information. Dividing video frames to reference and current frames, motion vectors and motion compensation residuals of current frames are estimated in regard to reference frames. The sparse codes of reference frames and motion compensation residuals are obtained using learned dictionaries, entropy-coded, and stored or sent to the receiver along with the coded motion field. In the receiver, after decoding the sparse codes and motion vectors, the reference frames and residuals are reconstructed employing the same learned dictionary and the current frames are recovered using the reference frames and motion fields. In the proposed scheme, the Iterative Least Square Dictionary Learning Algorithm (ILS-DLA) and K-SVD dictionary building methods are employed in the DCT domain. The compression rate and quality of the method based on the two dictionary learning algorithms are compared to each other and to H.264/AVC and HEVC modern standards. The results based on PSNR and SSIM criteria show that the proposed approach presents superior performance respect to H.264/AVC and even HEVC for higher bit-rates of QCIF video format, and the K-SVD learning algorithm performs slightly better than the ILS-DLA for the purpose.

Vascular diseases cause tortuosity in the retinal blood vessel's structure which can be identified using fundus images.The computerized retinal vessel tortuosity diagnosis is suffered from high time consuming and less accuracy due to the less effective retinal vessel segmentation algorithms.The success of retinal vessel tortuosity diagnosis depends on the performance quality of the vessel segmentation algorithm.Hence, this research proposes a new retinal vessel segmentation method, namely 'Retinal Vessel Segmentation using CLAHE and VJSTFD (RVSCV)'.The proposed segmentation method separates the vessel region from the background, tissue region, and Optic Disc (OD).It is constituted by two algorithms, viz.(i) vessel enhancement based on Contrast Limited Adaptive Histogram Equalization (CLAHE) and (ii) Vessel Joining algorithm based on vessel Skeletonization and Tetra vessel Flow Directions (VJSTFD).The CLAHE method, which is an existing method, enhances the vessel structure.The main contribution of this paper is the VJSTFD algorithm, which is a novel method to segment the vessel region from the enhanced fundus image.The VJSTFD algorithm makes a binary segmentation and joints the broken vessels in a novel approach through vessel skeletonization and tetra vessel flow directions-based vessel extension.The specialty of this approach is that minute vessels are also captured for segmentation even at the low contrast level because of the proposed preeminence vessel joining approach that is powered by tetra direction-based vessel searching.The CHASE_DB, RITE_DB, and STARE_DB databases have been involved in the testing process.These databases have retinal fundus images which clearly exposes the retinal vessel areas.Experimental results reveal that the proposed RVSCV method accomplishes the overall average F-score of 0.9580, along with the average segmentation accuracy of 96.73% in retinal vessel segmentation.The proposed method can be activated as a tool for ophthalmologists to extract the vessel course essentially.

Both interclass variances and intraclass similarities are crucial for improving the classification performance of discriminative dictionary learning (DDL) algorithms. However, existing DDL methods often ignore the combination between the interclass and intraclass properties of dictionary atoms and coding coefficients. To address this problem, in this paper, we propose a discriminative Fisher embedding dictionary learning (DFEDL) algorithm that simultaneously establishes Fisher embedding models on learned atoms and coefficients. Specifically, we first construct a discriminative Fisher atom embedding model by exploring the Fisher criterion of the atoms, which encourages the atoms of the same class to reconstruct the corresponding training samples as much as possible. At the same time, a discriminative Fisher coefficient embedding model is formulated by imposing the Fisher criterion on the profiles (row vectors of the coding coefficient matrix) and coding coefficients, which forces the coding coefficient matrix to become a block-diagonal matrix. Since the profiles can indicate which training samples are represented by the corresponding atoms, the proposed two discriminative Fisher embedding models can alternatively and interactively promote the discriminative capabilities of the learned dictionary and coding coefficients. The extensive experimental results demonstrate that the proposed DFEDL algorithm achieves superior performance in comparison with some state-of-the-art dictionary learning algorithms on both hand-crafted and deep learning-based features.

This study aimed to explore the effect of ultrasound imaging in the diagnosis and evaluation of acupoint application in the treatment of idiopathic edema. In this study, an ultrasound imaging diagnosis based on the segmentation dictionary learning (S-DL) algorithm was proposed. In addition, the autoencoding algorithm (ASE) was compared with the traditional dictionary learning (DL) algorithm. The treatment effect, associated quantitative integral, and quality of life score of patients in two groups were compared. The results showed that the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and structural similarity (SSIM) of the S-DL algorithm were 32.45 dB, 0.654, and 0.0012, respectively, which were quite different compared to the ASE and DL algorithms, showing statistical significance (P < 0.05). As the noise level increased, the image reconstruction quality gradually decreased, but the S-DL algorithm obtained better image quality than the DL and ASE algorithms, and the difference was statistically great (P < 0.05). There was no significant difference in the average age and average course of the disease between the experimental group and the control group (P > 0.05). The overall treatment effect of patients in the experimental group was 96.77%, while that in the control group was 45.16%, and the difference between the two was statistically significant (P < 0.05). After treatment, the semiquantitative scores of fatigue, dizziness, palpitation, frequent urination, urgent urination, and dyspepsia of the experimental group were 1.18, 0.39, 0.72, 1.21, and 0.87, respectively, which were much lower than those of the control group statistically (P < 0.05). The score of quality of life of the experimental group of patients after treatment was 91.27 points, and that of the control group was 82.35 points, showing statistically great difference (P < 0.05). It showed that the algorithm performance of S-DL was relatively good, and the acupoint application therapy was better than traditional western medicine in the treatment of idiopathic edema, which reduces the discomfort of patients to a certain extent and improves the quality of life of patients.

To speed up the convergence rate of learning dictionary in low bit-rate video coding, this paper proposes a spatio-temporal online dictionary learning (STOL) algorithm to improve the original adaptive regularized dictionary learning with K-SVD which involves a high computational complexity and interfere with the coding efficiency. Considering the intrinsic dimensionality of the primitives in training each series of 2-D sub dictionaries is low, the 3-D low-frequency and high-frequency dictionary pair would be formed by the online dictionary learning to update the atoms for optimal sparse representation and convergence. Instead of classical first-order stochastic gradient descent on the constraint set, e.g. K-SVD, the online algorithm would exploit the structure of sparse coding in the design of an optimization procedure in terms of stochastic approximations. It depends on low memory consumption and lower computational cost without the need of explicit learning rate tuning. Through drawing a cubic from i.i.d. samples of a distribution in each inner loop and alternating classical sparse coding steps for computing the decomposition coefficient of the cubic over previous dictionary, the dictionary update problem is converted to solve the expected cost instead of the empirical cost. For dynamic training data over time, online dictionary learning behaves faster than second-order iteration batch alternatives, e.g. K-SVD. Through experiments, the super-resolution reconstruction based on STOL obviously reduces the computational complexity to 40% to 50% of the K-SVD learning-based schemes with a guaranteed accuracy.

In this paper we show that the computational complexity of the iterative thresholding and K-residual-means (ITKrM) algorithm for dictionary learning can be significantly reduced by using dimensionality-reduction techniques based on the Johnson–Lindenstrauss lemma. The dimensionality reduction is efficiently carried out with the fast Fourier transform. We introduce the iterative compressed-thresholding and K-means (IcTKM) algorithm for fast dictionary learning and study its convergence properties. We show that IcTKM can locally recover an incoherent, overcomplete generating dictionary of $$K$$ atoms from training signals of sparsity level $$S$$ with high probability. Fast dictionary learning is achieved by embedding the training data and the dictionary into $$m< d$$ dimensions, and recovery is shown to be locally stable with an embedding dimension which scales as low as $$m = O(S\log ^4S\log ^3 K)$$. The compression effectively shatters the data dimension bottleneck in the computational cost of ITKrM, reducing it by a factor O(m/d). Our theoretical results are complemented with numerical simulations which demonstrate that IcTKM is a powerful, low-cost algorithm for learning dictionaries from high-dimensional data sets.

Most of the research on dictionary learning has focused on developing algorithms under the assumption that data is available at a centralized location. But often the data is not available at a centralized location due to practical constraints like data aggregation costs, privacy concerns, etc. Using centralized dictionary learning algorithms may not be the optimal choice in such settings. This motivates the design of dictionary learning algorithms that consider distributed nature of data as one of the problem variables. Just like centralized settings, distributed dictionary learning problem can be posed in more than one way depending on the problem setup. Most notable distinguishing features are the online versus batch nature of data and the representative versus discriminative nature of the dictionaries. In this paper, several distributed dictionary learning algorithms that are designed to tackle different problem setups are reviewed. One of these algorithms is cloud K-SVD, which solves the dictionary learning problem for batch data in distributed settings. One distinguishing feature of cloud K-SVD is that it has been shown to converge to its centralized counterpart, namely, the K-SVD solution. On the other hand, no such guarantees are provided for other distributed dictionary learning algorithms. Convergence of cloud K-SVD to the centralized K-SVD solution means problems that are solvable by K-SVD in centralized settings can now be solved in distributed settings with similar performance. Finally, cloud K-SVD is used as an example to show the advantages that are attainable by deploying distributed dictionary algorithms for real world distributed datasets.

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

Two common problems are often encountered in analysis dictionary learning (ADL) algorithms. The first one is that the original clean signals for learning the dictionary are assumed to be known, which otherwise need to be estimated from noisy measurements. This, however, renders a computationally slow optimization process and potentially unreliable estimation (if the noise level is high), as represented by the Analysis K-SVD (AK-SVD) algorithm. The other problem is the trivial solution to the dictionary, for example, the null dictionary matrix that may be given by a dictionary learning algorithm, as discussed in the learning overcomplete sparsifying transform (LOST) algorithm. Here we propose a novel optimization model and an iterative algorithm to learn the analysis dictionary, where we directly employ the observed data to compute the approximate analysis sparse representation of the original signals (leading to a fast optimization procedure) and enforce an orthogonality constraint on the optimization criterion to avoid the trivial solutions. Experiments demonstrate the competitive performance of the proposed algorithm as compared with three baselines, namely, the AK-SVD, LOST, and NAAOLA algorithms.

Dictionary learning (DL) for sparse coding has been widely applied in the field of computer vision. Many DL approaches have been developed recently to solve pattern classification problems and have achieved promising performance. In this paper, to improve the discriminability of the popular dictionary pair learning (DPL) algorithm, we propose a new method called discriminative dictionary pair learning (DDPL) for image classification. To achieve the goal of signal representation and discrimination, we impose the incoherence constraints on the synthesis dictionary and the low-rank regularization on the analysis dictionary. The DDPL method ensures that the learned dictionary has the powerful discriminative ability and the signals are more separable after coding. We evaluate the proposed method on benchmark image databases in comparison with existing DL methods. The experimental results demonstrate that our method outperforms many recently proposed dictionary learning approaches.

Dictionary learning is still a challenging problem in signal and image processing. In this paper, we propose an efficient block-structured incoherent dictionary learning algorithm for sparse representations of image signals. The constrained minimization of dictionary learning is achieved by iteratively alternating between sparse coding and dictionary update. Without relying on any prior knowledge of the group structure for the input data, we develop a two-stage clustering method that identifies the underlying block structure of the dictionary under certain restricted constraints. The two-stage clustering method mainly consists of affinity propagation and agglomerative hierarchical clustering. To meet the conditions of both the upper bound and the lower bound of the mutual coherence of dictionary atoms, we introduce a regularization term for the objective function to adjust the block coherence of the overcomplete dictionary. The experiments on synthetic data and real images demonstrate that the proposed dictionary learning algorithm has lower representation error, higher visual quality and better reconstructed results than most of the state-of-the-art methods.

Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically solve the problem by alternating between two stages: sparse coding and dictionary update. In this paper, we propose a novel dictionary learning algorithm using rank-one projection (ROP). The key contribution is that we cast dictionary learning as an optimization with respect to a single variable which is a set of rank one matrices. The resulting algorithm is hence single-stage. An alternating direction method of multipliers (ADMM) is derived to solve the optimization problem and a lower bound of penalty parameter is computed to guarantee a global convergence despite non-convexity of the optimization formulation. From practical point of view, ROP reduces the number of tuning parameters required in benchmark algorithms. Numerical tests demonstrate that ROP outperforms benchmark algorithms for both synthetic and real data.

Dictionary learning algorithms have received widespread acceptance when it comes to data analysis and signal representation problems. However, most existing algorithms assume isotropic noise. This is a restrictive assumption as the noise across samples may be nonuniform in a number of real world application. The aim of this article is to propose a sequential dictionary learning algorithm for measurement data vectors affected by nonuniform noise. As most of the existing algorithms, the proposed method is a two stages iterative algorithm where the effect of the noise nature appears in the sparse coding and dictionary update stages. The cost function used to derive the dictionary update stage is developed based on the link between singular value decomposition and rank one matrix approximation. Results on the simulated dictionary recovery problem and an application on face recognition dataset shows that the proposed algorithm outperforms current state of the art dictionary learning methods.

Fetal Heart Rate (FHR), an important recording in Cardiotocography (CTG)-based fetal health status monitoring, is the only information that clinical obstetricians can directly obtain and use. A challenge, however, is that missing samples are very common in FHR due to various causes such as fetal movements and sensor malfunctions. The aim is the development of an inpainting tool which is suitable for different missing lengths q and various total missing percentages Q, as well as for use in online mode. This study focused on two major impediments to existing inpainting methods: the longer the missing length, the more difficult it is to recover with mathematical methods; the reliance on tens of thousands of training samples, and the computational burden caused by full batch-based dictionary learning algorithms. We present a regularized minimization approach to signal recovery, which combines a L0.6 - norm minimized sparse dictionary learning algorithm (MSDL) and a model optimization strategy for using a mini-batch version for signal recovery. Using 100 FHR recordings with 2 protocols designed to simulate missing clinical data scenarios, the combined method performed favorably in terms of 5 data analysis metrics and 3 clinical indicators. Comparing 4 inpainting methods, we were able to prove the superiority of the proposed algorithm for both large q and large Q. The experimental results showed the lowest values (2.64 (MAE), 4.68 (RMSE)) when Q = 5% with short interval lengths. The developed architecture provides a reference value for the practical application of recovering missing samples online.

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data