Research On Modified Atching Pursuit Algorithms

There is no doubt that the proposal of Compressive Sensing is a significant event in the field of signal processing. What different from traditional Nyquist Sampling Theorem is that Compressive Sensing completes the procedure of compressing signals while sampling which can achieve signal sampling with a low sampling rate, relieving the pressure on hardware and reducing the cost of signal processing. Reconstruction Algorithms are necessary tools for Compressive Sensing to obtain final results and the study of Reconstruction Algorithms is a popular topic with high academic values as well as significance for popularizing the practical applications of Compressive Sensing. The dissertation consists of the following three aspects:(1) Introduced the basic theory and mathematical model of Compressive Sensing from the perspectives of sparse signal expansion theories, observing matrixes and reconstruction algorithms. Focused on reconstruction algorithms, especially MP algorithms including OMP, SP, SAMP and verified these algorithms with emulation.(2) With the introduction of algorithms’fusion, optimized the results of SAMP algorithm with the index sets of OMP algorithm and achieved promoting the reconstruction results of signals whose sparse degrees are unknown and calculated lifting range of performance. Besides, considering the initial index sets’great influence on reconstruction results of SP algorithm, we could improve algorithm results by assigning the initial sets manually. Under the idea, optimized the fusion result of SAMP and OMP further and improved the reconstruction quality. The emulation verified the feasibility of the algorithm.(3) The GOMP algorithm improved the efficiency of algorithm by iterating more than one atomic index in each iteration, however, it could only obtain one index set because the iterative process is of single-path. If there is any error existing in the iterative process, the final reconstruction result would be influenced greatly. The paper inherited the GOMP’s advantage of choosing multiple atomics and generated multiple candidate index set through iterations of multiple-path, selecting the one who minimized the residual signal as the final signal index set, and promoted the possibility of choosing correct index set. Also, the paper gave exact reconstruction conditions of the algorithm by mathematical proof. Besides, aiming at the disadvantage of large quantity of candidate index sets, optimized the method above further in a way of model strategy, and verified several index sets whose possibilities of correctness are larger, and selected the optimal one. It helped to avoid verifying meaninglessly those index sets whose possibility of correctness are not high and decreased the computational complexity in such way. Such GOMP of multiple-path can give consideration to the efficiency of algorithm and improve reconstruction results as much as possible simultaneously.