Regularization Parameter-Free Convolutional Sparse Coding via Projections Onto The ℓ1-Ball and The Discrepancy Principle

Given a set of dictionary filters, the most widely used formulation of the convolutional sparse coding (CSC) problem is convolutional basis pursuit denoising (CBPDN), in which an image is represented as a sum over a set of convolutions of coefficient maps. When the input image is noisy, CBPDN's...

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Published in:2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP) pp. 1 - 6
Main Author: Rodriguez, Paul
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2018
Subjects:
Convolution
Convolutional codes
Convolutional sparse coding
Encoding
Estimation
Image coding
Image reconstruction
Lasso
Morozov's discrepancy principle
Signal to noise ratio
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Abstract Given a set of dictionary filters, the most widely used formulation of the convolutional sparse coding (CSC) problem is convolutional basis pursuit denoising (CBPDN), in which an image is represented as a sum over a set of convolutions of coefficient maps. When the input image is noisy, CBPDN's regularization parameter greatly influences the quality of the reconstructed image. Results for an automatic and sensible selection of this parameter are very limited for the CSC / CBPDN case.In this paper we propose a regularization parameter-free method to solve the CSC problem via its projection onto the ℓ 1 -Ball formulation coupled with a warm-start like strategy, which, driven by the Morozov's discrepancy principle, adaptively increases/decreases its constrain at each major iteration. While the time performance of our proposed method is slower than that measured when solving CSC for a fixed regularization parameter, our computational results also show that our method's reconstruction quality is, in average, very close (within 0.16 SNR, 0.16 PSNR, 0.003 SSIM) to that obtained when the regularization parameter for CBPDN is selected to produce the best (SNR) quality result.
AbstractList Given a set of dictionary filters, the most widely used formulation of the convolutional sparse coding (CSC) problem is convolutional basis pursuit denoising (CBPDN), in which an image is represented as a sum over a set of convolutions of coefficient maps. When the input image is noisy, CBPDN's regularization parameter greatly influences the quality of the reconstructed image. Results for an automatic and sensible selection of this parameter are very limited for the CSC / CBPDN case.In this paper we propose a regularization parameter-free method to solve the CSC problem via its projection onto the ℓ 1 -Ball formulation coupled with a warm-start like strategy, which, driven by the Morozov's discrepancy principle, adaptively increases/decreases its constrain at each major iteration. While the time performance of our proposed method is slower than that measured when solving CSC for a fixed regularization parameter, our computational results also show that our method's reconstruction quality is, in average, very close (within 0.16 SNR, 0.16 PSNR, 0.003 SSIM) to that obtained when the regularization parameter for CBPDN is selected to produce the best (SNR) quality result.
Author Rodriguez, Paul
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  organization: Department of Electrical Engineering, Pontificia Universidad Católica del Perú, Lima, Peru
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Snippet Given a set of dictionary filters, the most widely used formulation of the convolutional sparse coding (CSC) problem is convolutional basis pursuit denoising...
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SubjectTerms Convolution
Convolutional codes
Convolutional sparse coding
Encoding
Estimation
Image coding
Image reconstruction
Lasso
Morozov's discrepancy principle
Signal to noise ratio
Title Regularization Parameter-Free Convolutional Sparse Coding via Projections Onto The ℓ1-Ball and The Discrepancy Principle
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