Overcomplete sparsifying transform learning algorithm using a constrained least squares approach

Ekşioğlu, Ender M.; Bayir, Ozden

doi:10.1109/icassp.2014.6854989

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…In addition, we compare our algorithm MADL with some state-of-the-art algorithms, namely, AOL [27], transform K-SVD (TKSVD) [45], and constrained-least-squares sparsifying transform learning (CLS-TL) [46], all of which involve the orthogonality constraint on the analysis dictionary. The results are shown in Fig.…”

Section: Figurementioning

confidence: 99%

“…The test images are obtained from the Yale face database 2 . We compare the denoising performance for images using a learned dictionary and a finite difference (FD) operator [47], and we compare the algorithm MADL with the advanced algorithms AOL [27], TKSVD [45], and CLS-TL [46] to assess the efficiency of the proposed algorithm. In our experiments, we set the parameter of the Douglas-Rachford algorithm to µ = 0.0002 (in Algorithm 2).…”

Section: B Image Denoising With the Learned Dictionarymentioning

confidence: 99%

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Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold

Ding

Tan

et al. 2019

IEEE Access

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Sparse representation with an analysis model becomes a challenging task because the optimization problem involves additional constraints on the analysis dictionary. We present the problem of learning the analysis dictionary through an optimization function with an orthogonality constraint, which can be generally solved by alternately implementing the analysis dictionary update and the sparse coding steps. In the dictionary update step, the traditional method for updating the analysis dictionary with the orthogonality constraint is to first perform the update in Euclidean space without taking the constraint into consideration and then project the solution onto a manifold where the orthogonality constraint is satisfied. However, this projection method is approximate, and the learned dictionary obtained by projection may not embody the inherent structure of the original dictionary. Thus, we develop a novel framework for seamlessly learning the analysis dictionary along with the manifold. This method can provide a more accurate and effective analysis dictionary. In the sparse coding problem, to avoid adjustment of the parameters of the formulation, we introduce an indicator function as the penalty function for optimization of the cost function. Thus, we reduce two parameters to one, which is easier to optimize. Then, we adopt a Douglas-Rachfordlike scheme to solve the problem. From the results of the numerical experiments conducted to evaluate the recovery rate of the analysis dictionary, we can intuitively see the performance of the proposed algorithms. Furthermore, the proposed algorithms show good performance in image denoising for realistic applications.

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Section: Figurementioning

confidence: 99%

Section: B Image Denoising With the Learned Dictionarymentioning

confidence: 99%

Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold

Ding

Tan

et al. 2019

IEEE Access

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“…Both of the subproblems (9a) and (9b) have exact, closed form solutions [27]. The solution for (9a) can be given as ΩX β , where • β denotes the elementwise soft thresholding operation [29]. The soft thresholded result is calculated as follows.…”

Section: Patch-wise Regularization: Updating ω Andxmentioning

confidence: 99%

MRI reconstruction with joint global regularization and transform learning

Tanc

Ekşioğlu

2016

Computerized Medical Imaging and Graphics

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Sparsity based regularization has been a popular approach to remedy the measurement scarcity in image reconstruction. Recently, sparsifying transforms learned from image patches have been utilized as an effective regularizer for the Magnetic Resonance Imaging (MRI) reconstruction. Here, we infuse additional global regularization terms to the patch-based transform learning. We develop an algorithm to solve the resulting novel cost function, which includes both patchwise and global regularization terms. Extensive simulation results indicate that the introduced mixed approach has improved MRI reconstruction performance, when compared to the algorithms which use either of the patchwise transform learning or global regularization terms alone.

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“…Both (P2.1.1) and (P2.1.2) have closed form solutions [9]. (P2.1.1) is solved by simple soft thresholding [11]. The solution for (P2.1.2) involves an SVD over the matrix L −1X A H , where L is the solution toXX H + λI = LL H .…”

Section: The G-tlmri Algorithmmentioning

confidence: 99%

Transform learning MRI with global wavelet regularization

Tanc

Ekşioğlu

2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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Sparse regularization of the reconstructed image in a transform domain has led to state of the art algorithms for magnetic resonance imaging (MRI) reconstruction. Recently, new methods have been proposed which perform sparse regularization on patches extracted from the image. These patch level regularization methods utilize synthesis dictionaries or analysis transforms learned from the patch sets. In this work we jointly enforce a global wavelet domain sparsity constraint together with a patch level, learned analysis sparsity prior. Simulations indicate that this joint regularization culminates in MRI reconstruction performance exceeding the performance of methods which apply either of these terms alone.

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Overcomplete sparsifying transform learning algorithm using a constrained least squares approach

Cited by 7 publications

References 18 publications

Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold

Sparse Representation Based on the Analysis Model With Optimization on the Stiefel Manifold

MRI reconstruction with joint global regularization and transform learning

Transform learning MRI with global wavelet regularization

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