Learning Sparsifying Transforms

Ravishankar, S.; Bresler, Yoram

doi:10.1109/tsp.2012.2226449

Cited by 328 publications

(428 citation statements)

References 41 publications

Supporting

Mentioning

419

Contrasting

Unclassified

Order By: Relevance

“…There are two well known sparsity models [8] to which the dictionary learning approach is applied. One is the synthesis sparsity model which states that a linear combination of a few of the dictionary atoms is sufficient to represent the signal [8] [9]. The other is analysis sparsity model which suggests that the representation of a signal in the dictionary is sparse [8] [9].…”

Section: Introductionmentioning

confidence: 99%

“…One is the synthesis sparsity model which states that a linear combination of a few of the dictionary atoms is sufficient to represent the signal [8] [9]. The other is analysis sparsity model which suggests that the representation of a signal in the dictionary is sparse [8] [9]. Ravishankar and Bresler explored the transform sparsity model and proposed a parameter dependent transform learning (TL) method for square transforms in [9], for orthogonal transforms (TLortho) in [11] and for overcomplete transforms in [10].…”

Section: Introductionmentioning

confidence: 99%

“…The other is analysis sparsity model which suggests that the representation of a signal in the dictionary is sparse [8] [9]. Ravishankar and Bresler explored the transform sparsity model and proposed a parameter dependent transform learning (TL) method for square transforms in [9], for orthogonal transforms (TLortho) in [11] and for overcomplete transforms in [10]. In [12], Eksioglu et al proposed a parameter independent transform learning method called the Transform K-SVD (T-KSVD).…”

Section: Introductionmentioning

confidence: 99%

“…The condition number of the transform and the compressibility of the signals relative to the transform generated by TL algorithm [9] depend strongly on the parameters chosen. The orthogonal transform learning of [11] is parameter independent and gives good performance in attaining the specified sparsity.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm proposed in this paper is inspired by the methods proposed in [9], [11], [12] and [13]. The proposed algorithm (section III) is to learn a square sparsifying transform for a class of signals from a known non-sparsifying transform.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transform learning algorithm based on the probability of representation of signals

Parthasarathy

Abhilash

2017

2017 25th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

show abstract

Block‐matching sparsity regularization‐based image reconstruction for low‐dose computed tomography

Cai

Zheng

et al. 2018

Medical Physics

View full text Add to dashboard Cite

show abstract

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

2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Learning Sparsifying Transforms

Cited by 328 publications

References 41 publications

Transform learning algorithm based on the probability of representation of signals

Transform learning algorithm based on the probability of representation of signals

Block‐matching sparsity regularization‐based image reconstruction for low‐dose computed tomography

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

Contact Info

Product

Resources

About