The Recovery Algorithm Of Compressed Sensing With Chirp Matrix

Deterministic compressed sensing are becoming the research focus for their sensingmatrices can be generated from just several parameters. A matrix with chirp rate and basefrequency increasing is determined only by signal’s length and measurements number.Besides, only need generate these chirp sequences related to nonzero locations instead of thewhole sensing matrix, more importantly, we can accelerate reconstruction process by FFT dueto the structure of chirp matrices. Both the reconstruction time and storage space are reducedwhen compared to other CS methods with deterministic matrices.This paper researches on how to relax the sparsity condition of CS with chirp matricesand reduce the reconstruction error. The main work is as follows:1. For the correlation DFT method requires signal must have a low sparsity and its poorreconstruction accuracy, a DCFT based reconstruction algorithm is proposed. Compared tocorrelation DFT, the DCFT with enhanced chirp rate has less cross modulation interference.Thus it has a larger probability to locate the nonzero items by the cordinates of the maximumamplitude. Meanwhile, with the sparsity increasing, make the measurement signals themselfhave much information enough to reconstruct via increasing the measurement number.Sampling and reconstruction experiments of one-dimensional signals show that thereconstruction error of proposed algorithm with a iterative pace of1/2square root of themeasurement number are less than that of correlation DFT algorithm with a fixedmeasurement number, and the reconstruciton time just increases slowly and steadily as thesparsity increases.2. For these sparse natural images, a DCFT and correlation DFT joint algorithm withvariable approximation component estimation is proposed. Arrange the image waveletcoefficients to form a vector in the order of approximate, horizontal, vertical and detailcomponents and measure them by4chirp-rates’ matrix. As the sparsing and energyaggregation feature of wavelet transform, detecting multiple cofficients during each iterationof DCFT, and the correlation DFT’s advantage of detecting little coefficients, use theApproximate Component Estimation, DCFT and correlation DFT methods to locate nonzero coefficients respectively. The experiments of different images show that the proposedalgorithm is superior to subspace pursuit in the aspect of reconstruction error and imagequality.3. For the false detected number and reconstruction time increase significantly followedas the nonzero number increase in DCFT-correlation DFT joint algorithm, a DCFT iterationalgorithm with context contraint is proposed. As the DCFT detects nonzero coefficientsiteratively and the least square method distributes automatically the accurate value to everycoefficients detected, we can view these coefficients of which relative variation between twoneighbouring iterations exceed a threshold value predetermined as the false detectedcoefficients, and remove them from the matching set. Experiments show that both the numberof false detected coefficients and the reconstruction time of the DCFT algorithm with contextconstraint decrease significantly.