Research On Multi-candidate Orthogonal Matching Pursuit Improved Algorithm Based On Compressed Sensing

Compressed sensing (CS), proposed by Candes, Donoho in 2004, is a new signal acquisition, encoding and decoding theory which takes advantage of signal sparsity. CS obtain discrete samples of the signal at a rate much less than the sampling rate specified conditions of the Nyquist sampling theorem, the signal is non-adaptive coding measurements. CS decoding process is not the inverse of the encoding process, but in the sense of probability to perfect reconstruct the signal by non-linear reconstruction algorithm or reconstruct the signal at a certain approximation errors. Compressed sensing theory includes three core contents:Sparse signal representation, coding measurement and signal reconstruction. Signal reconstruction algorithm is a key step to determine if compressed sensing can be applied to an actual system. This thesis starts an in-depth research in greedy iterative reconstruction algorithm with CS theoretical as the framework. Two improved algorithms are given and are used to deal with one-dimensional and two-dimensional signal reconstruction process.The main work is as follows:This thesis first discusses the purpose of studying compressed sensing theory, before introducing some current researches in recent years. Then we make a full description of the compressed sensing three core contents. Then this thesis introduces some key notions as orthogonal matching pursuit(OMP) algorithm, multi-candidate orthogonal matching pursuit(MOMP) algorithm and so on with a theory based on matching pursuit reconstruction algorithms. A comparative study between the algorithms were also given, in which their respective advantages and disadvantages were detailed upon. In order to improve the reconstruction quality, the thesis introduces the atoms matching based on Dice coefficient criterion locate residual signal main component quickly, alternatives to traditional rule of inner product similarity measure method, applying it to MOMP algorithm, get new DMOMP algorithm. Through simulating and comparing the probability of the successful reconstruction, reconstruction time, the reconstruction error of a one-dimensional signal show that DMOMP can effectively improve the performance advantages of MOMP algorithm. The thesis improves the iteration stop condition of DMOMP algorithm, the residual two-norm less than a particular value as the iteration stop condition, give M-DMOMP algorithm to solve the problem which is DMOMP algorithm iterations limited by sparsity. Finally M-DMOMP algorithm, DMOMP algorithm and DOMP algorithm are applied to reconstruct two-dimensional image to prove that improve the image reconstruction quality when the algorithm iterations without signal sparsity constraints.