K-SVD Meets Transform Learning: Transform K-SVD

Ekşioğlu, Ender M.; Bayir, Ozden

doi:10.1109/lsp.2014.2303076

Cited by 41 publications

(43 citation statements)

References 9 publications

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“…In this section, we demonstrate the potential of the transform generated using the PTL algorithm proposed in this paper in comparison with the transforms generated using the TL algorithm [9], the T-KSVD algorithm [12], the TLortho algorithm [11] and the Principal component analysis (PCA). The TL and TLortho were studied experimentally using the softwares available in [23] and T-KSVD algorithms using the software available in [24], respectively.…”

Section: Resultsmentioning

confidence: 99%

“…The TL and TLortho were studied experimentally using the softwares available in [23] and T-KSVD algorithms using the software available in [24], respectively. The values of the parameters used in the TL algorithm were chosen so as to generate a well conditioned transform, that is, the weight of log determinant penalty and Forbenius norm penalty were 10 5 .…”

Section: Resultsmentioning

confidence: 99%

“…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 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%

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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: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…This model can be regarded as a natural extension of the sparse analysis model. Learning a sparsifying transform has been investigated in [7], [20], [21]. These algorithms deal with the sparsification error in the transform domain rather than in the original signal domain as in the ADL algorithms [17], [18], by applying the transform operator to the training signals even if the signals contain noise.…”

Section: B Sparse Analysis Model and Sparsifying Transform Modelmentioning

confidence: 99%

Analysis SimCO Algorithms for Sparse Analysis Model Based Dictionary Learning

Dong

Wang

Dai

et al. 2016

IEEE Trans. Signal Process.

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Abstract-In this paper, we consider the dictionary learning problem for the sparse analysis model. A novel algorithm is proposed by adapting the simultaneous codeword optimization (SimCO) algorithm, based on the sparse synthesis model, to the sparse analysis model. This algorithm assumes that the analysis dictionary contains unit ℓ2-norm atoms and learns the dictionary by optimization on manifolds. This framework allows multiple dictionary atoms to be updated simultaneously in each iteration. However, similar to several existing analysis dictionary learning algorithms, dictionaries learned by the proposed algorithm may contain similar atoms, leading to a degenerate (coherent) dictionary. To address this problem, we also consider restricting the coherence of the learned dictionary and propose Incoherent Analysis SimCO by introducing an atom decorrelation step following the update of the dictionary. We demonstrate the competitive performance of the proposed algorithms using experiments with synthetic data and image denoising as compared with existing algorithms.

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