Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model

Rubinstein, Ron; Peleg, Tomer; Elad, Michael

doi:10.1109/tsp.2012.2226445

Cited by 424 publications

(389 citation statements)

References 24 publications

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“…As mentioned in section II, it is not possible to obtain the extreme entropy minimization for the class of signals because H(c) > 0. Hence, the basis vector obtained as a solution to (6) need not capture all the information present in the class of signals. Though we expect most of the information to be captured by ψ 1 , practically that is not possible and its probability of representation in a few of the signals will be small.…”

Section: A the Algorithmmentioning

confidence: 99%

Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Compressed sensing is a signal acquisition scheme that measures signals at sub-Nyquist rate amenable to sparse recovery, with high probability, from a reduced set of measurements. One of the main requirements of compressive sensing is the sparsity of the class of signals of interest in some basis. A method to construct a sparsifying basis for a class of signals using information theoretic measures is proposed in this paper. The algorithm constructs the sparsifying basis from a known nonsparsifying basis by concentrating the probability distribution of the basis in the representation of a class of signals. Simulation studies using speech and image signals confirm that the basis constructed using the proposed method results in an improved sparsity of the signals with thresholded coefficients but without degrading the signal quality.

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Section: A the Algorithmmentioning

confidence: 99%

Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…In this section, we present a subset pursuit algorithm for ADL by directly using the observed data without having to pre-estimate X (as done in [18]). More specifically, we exploit the analysis representation of Y to obtain the subset Y j rather than using the estimation of X to determine Y j .…”

Section: Subset Pursuit Algorithm For Analysis Dictionary Learningmentioning

confidence: 99%

“…is the initial dictionary in which each row is orthogonal to a random set of M − 1 training data and is also normalized [18].…”

Section: Computer Simulationsmentioning

confidence: 99%

“…In the experiments, we use the same experiment protocol as in [18]. Ω ∈ R 50×25 is generated with random Gaussian entries and the training dataset consists of K = 50000 signals for each co-rank l = 21 with both a noise-free setup and a noisy setup (σ = 0.04,SNR = 25 dB).…”

Section: Recovering the Ground-truth Analysis Dictionarymentioning

confidence: 99%

“…In the WSBI algorithm, the parameters are set as η = 0.1, ρ = 10 The parameters of the SBI algorithm are the same as those in the WSBI algorithm. In the OBG algorithm, the parameters are set as those originally suggested in [18]. The results, averaged over five trials, are presented in Table 2 and Table 3.…”

Section: Experiments For the Wsbi Algorithmmentioning

confidence: 99%

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Analysis Sparse Representation Based on Subset Pursuit and Weighted Split Bregman Iteration Algorithm

Zhang

2015

International Journal of Advanced Robotic Systems

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Recently, a sparse representation model -called an analysis sparse model -where the signal is multiplied by an analysis dictionary and the outcome is assumed to be sparse, has received increasing attention since it has potential and extensive applications in the area of signal processing. The performance of the analysis model significantly depends on an appropriately chosen dictionary. Most existing analysis dictionary learning algorithms are based on the assumption that the original signals are known or can be estimated from their noisy versions. Generally, however, the original signals are unknown or need to be estimated by using greedy-like algorithms with heavy computation.To solve the problems, we introduce a subset pursuit algorithm for analysis dictionary learning, where the observed signals are directly employed to learn the analysis dictionary. Next, a weighted split Bregman iteration algorithm is proposed to estimate original signals by the learned analysis dictionary. The experimental results demonstrate the competitive performance of the proposed algorithms compared with the state-of-art algorithms.

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Multilayer residual sparsifying transform (MARS) model for low‐dose CT image reconstruction

2021

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Purpose Signal models based on sparse representations have received considerable attention in recent years. On the other hand, deep models consisting of a cascade of functional layers, commonly known as deep neural networks, have been highly successful for the task of object classification and have been recently introduced to image reconstruction. In this work, we develop a new image reconstruction approach based on a novel multilayer model learned in an unsupervised manner by combining both sparse representations and deep models. The proposed framework extends the classical sparsifying transform model for images to a Multilayer residual sparsifying transform (MARS) model, wherein the transform domain data are jointly sparsified over layers. We investigate the application of MARS models learned from limited regular‐dose images for low‐dose CT reconstruction using penalized weighted least squares (PWLS) optimization. Methods We propose new formulations for multilayer transform learning and image reconstruction. We derive an efficient block coordinate descent algorithm to learn the transforms across layers, in an unsupervised manner from limited regular‐dose images. The learned model is then incorporated into the low‐dose image reconstruction phase. Results Low‐dose CT experimental results with both the XCAT phantom and Mayo Clinic data show that the MARS model outperforms conventional methods such as filtered back‐projection and PWLS methods based on the edge‐preserving (EP) regularizer in terms of two numerical metrics (RMSE and SSIM) and noise suppression. Compared with the single‐layer learned transform (ST) model, the MARS model performs better in maintaining some subtle details. Conclusions This work presents a novel data‐driven regularization framework for CT image reconstruction that exploits learned multilayer or cascaded residual sparsifying transforms. The image model is learned in an unsupervised manner from limited images. Our experimental results demonstrate the promising performance of the proposed multilayer scheme over single‐layer learned sparsifying transforms. Learned MARS models also offer better image quality than typical nonadaptive PWLS methods.

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Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model

Cited by 424 publications

References 24 publications

Transform learning algorithm based on the probability of representation of signals

Transform learning algorithm based on the probability of representation of signals

Analysis Sparse Representation Based on Subset Pursuit and Weighted Split Bregman Iteration Algorithm

Multilayer residual sparsifying transform (MARS) model for low‐dose CT image reconstruction

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