Learning Sparsifying Transforms

The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionari...

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Bibliographic Details
Published in:	IEEE transactions on signal processing 2013-03, Vol.61 (5), p.1072-1086
Main Authors:	Ravishankar, S., Bresler, Y.
Format:	Article
Language:	eng
Subjects:	Algorithm design and analysis Analytical models Applied sciences Biological and medical sciences Compressed sensing Computerized, statistical medical data processing and models in biomedicine Detection, estimation, filtering, equalization, prediction Dictionaries dictionary learning Encoding Exact sciences and technology Image processing Information, signal and communications theory Medical management aid. Diagnosis aid Medical sciences Noise measurement Signal analysis Signal and communications theory signal denoising Signal processing Signal representation. Spectral analysis Signal, noise sparse representation sparsifying transforms Telecommunications and information theory Transforms
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Summary:	The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising, inpainting, and medical image reconstruction. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. In this work, we propose novel problem formulations for learning sparsifying transforms from data. The proposed alternating minimization algorithms give rise to well-conditioned square transforms. We show the superiority of our approach over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in signal denoising using the learnt sparsifying transforms. The proposed approach is much faster than previous approaches involving learnt synthesis, or analysis dictionaries.
ISSN:	1053-587X 1941-0476