Using reed-muller sequences as deterministic compressed sensing matrices for image reconstruction

An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order ReedMuller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an efficient 2D CS algorithm using RM sequences, provides medical image reconstruction examples, and compares it with the original 2D CS using noiselets. This algorithm entails several innovations that enhance its suitability for images: initial best approximation, a greedy algorithm for the nonzero locations, and a new approach in the least-squares step. These enhancements improve fidelity, execution time, and stability in the context of image reconstruction.

• Type: Journal
• Year: 2010
• Where: ICASSP
• Authors: Kangyu Ni, Somantika Datta, Prasun Mahanti, Svetlana Roudenko, Douglas Cochran
• Keywords: Algorithm, ICASSP 2010, Image Reconstruction, RM Sequences, Signal Processing