Sparse Decomposition of Two Dimensional Signals

A. Ghafari (1) , Massoud Babaie-Zadeh (1) , Christian Jutten (2)

1 EE department of SUT [Tehran] - Department of Electrical Engineering [Tehran]
2 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique

In this paper, we consider sparse decomposition (SD) of twodimensional (2D) signals on overcomplete dictionaries with separable atoms. Although, this problem can be solved by converting it to the SD of one-dimensional (1D) signals, this approach requires a tremendous amount of memory and computational cost. Moreover, the uniqueness constraint obtained by this approach is too restricted. Then in the paper, we present an algorithm to be used directly for sparse decomposition of 2D signals on dictionaries with separable atoms. Moreover, we will state another uniqueness constraint for this class of decomposition. Our algorithm is obtained by modifying the Smoothed L0 (SL0) algorithm, and hence we call it two-dimensional SL0 (2D-SL0).

Keywords: Image Coding; Sparse Coding; Compressive Sensing; Sparse Decomposition; Sparse Representation

Domains: Signal and Image Processing; Signal and Image processing

A. Ghafari, Massoud Babaie-Zadeh, Christian Jutten. Sparse Decomposition of Two Dimensional Signals. ICASSP 2009 - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2009, Taipei, Taiwan. pp.3157-3160. ⟨hal-00400464⟩