Research On Generalized Orthogonal Matching Pursuit Algorithm Based On Compressed Sensing

Compressed sensing theory is an emerging signal sampling and compression technology which is a breakthrough to Nyquist sampling theory. It overcomes the limitation that the sampling rate is limited to the bandwidth of the signal. Instead, the signal sampling rate depends only on the signal itself. Compressed sensing theory adopts the sparse representation of signal and recovers the original signal from less observed value. It includes the selection of signal sparse representation, measurement matrix and reconstruction algorithm, As an important part of the reconstruction algorithm, the objective of compressed sensing reconstruction algorithm is to get the best reconstruction quality with the least cost.The main work of this thesis is as follows:1. Introduces four kinds of reconstruction algorithm of greedy algorithm, they are:orthogonal matching pursuit algorithm, regularized orthogonal matching pursuit algorithm, compressed sampling matching pursuit algorithm and generalized orthogonal matching pursuit algorithm. And the simulation of these typical greedy algorithms are compared and analyzed due to signal reconstruction success rate under the different observation dimension and different degrees of sparse. The experiment results show that the reconstruction effect of generalized orthogonal matching pursuit algorithm is the best in signal reconstruction success rate.2. Because of the measure of signals similarity, the inner product method can not reflect the effection of amplification data important component. Therefore, the Dice coefficient criterion is introduced to measure the matching degree of atomic and residual signal. Generalized orthogonal matching pursuit algorithm based on Dice coefficient criterion algorithm is obtained through inserting Dice sparse into generalized orthogonal matching pursuit algorithm. The simulation of signal reconstruction success rate, signal reconstruction error and signal reconstruction time to compare generalized orthogonal matching pursuit algorithm based on Dice coefficient criterion and generalized orthogonal matching pursuit algorithm illustrate the feasibility of the generalized orthogonal matching pursuit algorithm based on Dice coefficient criterion. The two-dimensional image Lena and Cameraman images are reconstructed by using generalized orthogonal matching pursuit algorithm based on Dice coefficient criterion and regularized orthogonal matching pursuit based on Dice coefficient criterion, reconstruction time, reconstruction error and reconstructed image quality are compared under different sampling rate. The experiments show that the reconstructed image quality through regularized orthogonal matching pursuit algorithm based on Dice coefficient criterion algorithm and compressed sampling matching pursuit based on Dice coefficient criterion algorithm is superior to that through generalized orthogonal matching pursuit algorithm and regularized orthogonal matching pursuit algorithm.