Research On Reconstruction Algorithms And Applications Of Compressed Sensing

Compressed sensing (CS) is a breakthrough in signal acquisition field, which switchessignal acquisition into information acquisition by taking signal’s sparsity into account, andcan recover original signal from its a fewer samples. This theory has broad applications, andin this paper, we mainly research the signal reconstruction algorithms and its application inimage.The theory frame of CS includes signal sparse representation, measurement matrix andsignal reconstruction. Rigorous sparse signal is nearly impossible in nature, so it’s necessaryto represent signals in sparse forms, available means includes transform in orthogonal basicsand representation in redundant dictionaries. The restricted isometry property is an importantindicator of measurement matrix, and most random matrices contain this property thereforecan be used in CS. Recovery algorithms fall into three rough categories: convex relaxation,greedy pursuits and combinational algorithms. We mainly study basis pursuit, OMP and othermodified versions.Then we propose a new greedy reconstruction algorithm termed Optimised StagewiseOrthogonal Matching Pursuit (OSOMP), which is an improved version for StOMP. InOSOMP, a crop operation is introduced where a small proportion of selected atoms arediscarded according to the amplitude of estimated signal, thus if an atom is wrongly selected,then it will be swept away in later iterations with high possiblity. Theoretical analysis andsimulation experiments show that, OSOMP discardes most false dicovered atoms in cropoperation which improves the accuracy of atom set, so it enjoys higher recovery performancein both sparse and compressible signals, and still suits for large scale problems because theconvergency rate is kept well.In terms of application, we propose an image compressed sensing and reconstructionalgorithm based on chaos. In this algorithm, original image is divided into small blocks andtranformed into sparse basis, then the coefficients are disturbed by a chaos sequence andmeasured by the same measurement matrix. Compared to original algorithm, the chaosdisturbance can make the sparsity of each block’s coefficients comes closer, therefore allblocks can be properly measured by a same matrix and enjoy almost equal recovery quality, so the blocking effect is limited and the total reconstruction performance is improved underthe same sampling rate.