Research On Reconstruction Algorithms And Application Based On Compressed Sensing

Compressive sensing(CS) theory is an important progress in signal acquisition field, which beyond the limitation of sampling theorem by taking the sparsity of signal into account. It can achieve an accurate reconstruction from fewer samples, which saves the resources for storage and transmission of information resources, and therefore CS has broad application prospects. This paper studies the theoretical framework of CS from sparse representation of signal and the design of measurement matrix to reconstruction algorithm, focusing on the reconstruction algorithm, we propose CNSL0 algorithm and CDNSL0 algorithm. It takes good results while applying to image compressed sampling, which is proved by a series of experiments.The CNSL0 algorithm and CDNSL0 algorithm are based on the SL0 algorithm. The main idea of SL0 algorithm is to find a smooth continuous function to replace ?0 norm approximately, and then takes advantage of the steepest descent method and gradient projection principle to approximate optimal solution. CNSL0 algorithm takes steeper function than SL0, overcomes the aliasing problem by using modified Newton method and eliminates the existence of an infinite loop in NSL0 algorithm by introducing a threshold. CDNSL0 algorithm is proposed as the supplement of CNSL0 algorithm to overcome the divergence by using damped Newton Method. The experimental results show that the CNSL0 algorithm is more accurate, faster and more robust than SL0 algorithm.Since most images are compressible in wavelet transform domain, CNSL0 algorithm can be applied to image compressed sampling. CNSL0 algorithm applies to the reconstruction of one-dimensional signal, so it should use CNSL0 algorithm column by column for image reconstruction. The whole process would be as follows. Firstly, choose proper wavelet transform matrix for the image to make sure that it’s compressible. Secondly, sample the image by proper measurement matrix. Thirdly,find the sparse representation for the sampled image in wavelet transform domain. Finally, take inverse wavelet transform to get original image. In order to analysis the algorithms completely, this thesis designs four experiments, including noiseless measurement under same compression ratio, noisy measurement under same compression ratio, noiseless measurement under different compression ratio and noise measurement under different compression ratio. The experimental results show that the CNSL0 algorithm is faster and more robust than SL0 algorithm, and the reconstructed image holds higher peak signal to noise rate.