A new greedy sparse recovery algorithm for fast solving sparse representation

Abstract

Kernel sparse representation-based classification (KSRC) in compressive sensing represents one of the most interesting research areas in pattern recognition and image processing. Nevertheless, KSRC is subjected to some shortcomings. KSRC is greedy in time to achieve an approximate solution of sparse representation based on $$\ell_{1}$$ -norm minimization. A diversity of greedy recovery algorithms have been tested in order to decrease computational complexity compared to the optimal $$\ell_{1}$$ -norm minimization while keeping a proved reconstruction accuracy. In this research, we suggest a new greedy recovery algorithm, called the fast reduced sampling matching pursuit (FRSMP). Unlike previous greedy recovery algorithms which applied too many or very few values per iteration, FRSMP selects a sufficient number of elements. Moreover, FRSMP performs the least square minimization iteratively through the Sherman–Morrison–Woodbury formula, to avoid large matrix inversion which results in a significant speedup. Experimental results with both noisy and noiseless data have shown that the proposed FRSMP method achieves a higher reconstruction accuracy at low reconstruction time compared to other greedy pursuit algorithms. Also, experiments on frequent face databases have proven that the KSRC-based FRSMP method shows reliable and higher recognition rate and computation time compared with other advanced sparse representation methods for face recognition.