Oblique Projection Matching Pursuit

Recent theory of compressed sensing (CS) tells us that sparse signals can be reconstructed from a small number of random samples. In reconstruction of sparse signals, greedy algorithms, such as the orthogonal matching pursuit (OMP), have been shown to be computationally efficient. In this paper, the performance of OMP is shown to be dependent on how well information of the underlying signals is preserved in the residual vector. Further, to improve the information preservation, we present a modification of OMP, called oblique projection matching pursuit (ObMP), which updates the residual in a oblique projection manor. Using the restricted isometric property (RIP), we build a solid yet very intuitive grasp of the more accurate phenomenon of ObMP. We also show from empirical experiments that the ObMP achieves improved reconstruction performance over the conventional OMP algorithm in Feng Wang [email protected] Jian Wang [email protected] Yunquan Dong [email protected] Byonghyo Shim [email protected] 1 Department of Electrical and Computer Engineering, Seoul National University, Seoul, Korea 2 School of Industrial Management Engineering, Korea University, Seoul, Korea 3 School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China terms of support detection ratio and mean squared error (MSE).