Biblio

Sparse representation of signals based on redundant dictionary is widely used in array signal processing. In this paper, a redundant dictionary construction method via genetic algorithm (GA) is proposed for array signal processing. The problem is formulated as a dictionary selection problem where the dictionary entries are produced by discretizing the angle space. We apply the orthogonality of the entries to evaluate the dictionary according to the Restricted Isometry Property (RIP). GA is used to discretize the angle space which can make the dictionary more orthogonal. Simulation results show that the proposed method can obtain a better division of angle, improving the orthogonality of dictionary effectively, and is suitable for arbitrary observation space compared with commonly used equal angle division and equal sine division.

This paper proposes a fast and robust procedure for sensing and reconstruction of sparse or compressible magnetic resonance images based on the compressive sampling theory. The algorithm starts with incoherent undersampling of the k-space data of the image using a random matrix. The undersampled data is sparsified using Haar transformation. The Haar transform coefficients of the k-space data are then reconstructed using the orthogonal matching Pursuit algorithm. The reconstructed coefficients are inverse transformed into k-space data and then into the image in spatial domain. Finally, a median filter is used to suppress the recovery noise artifacts. Experimental results show that the proposed procedure greatly reduces the image data acquisition time without significantly reducing the image quality. The results also show that the error in the reconstructed image is reduced by median filtering.