Research On Reconstruction Of Signal And Image Based On Gradient-based Algorithm In Cs

The datum acquisition of Shannon sampling theorem is just a bandwidth basedlocal sampling process, which needs the sampling rate to be equal or greater thantwice of the bandwidth to fully recover original signal. However modem signalprocessing requires more and more high sampling rate, so it brings great challenges totraditional information acquisition. On the other hand, if we want to acquire signal inmore detail, we need sample more datum; for economical datum transmission andstorage, we need compress and discard more datum.Compressive sensing(CS) transfers its research from bandwidth to the structureof signal. While signal is sparse in some transform domain, we can acquire the signalwith a measurement matrix incoherent to transform bases at a rate significantly lowerthan Nyquist rate. So CS can compress the acquired datum while sampling, thenreconstruct the original signal via optimization without any information loss.In this paper, I will employ l1norm based model for signal recovery on the basisof analyzing the advantages and disadvantages of existing recovery model. Buttraditional algorithms of l1norm based model can’t be used for large scale datumprocessing. For this problem, from gradient descent method, we obtain iterativeshrinkage thresholding(IST) algorithm which is a gradient-based recovery algorithm.This method owns a low computational complexity, which could not be utilized inlarge datum processing but also has a fast convergence rate. Based on deeplyanalyzing factors influencing the reconstruction, this paper concludes thatregularization model and parameter λ significantly determine the recovery effect.However the existing random measurement matrices are complex, so this paperproposes a new measurement matrix. Its generation method is very simple and it canobtain a good reconstruction in comparison with Gaussian matrix in the samecondition but owns a faster reconstruction rate. At last, introduce improved ISTmethod called fast IST, which improves convergence rate from O(k-1) to O(k-2).The existing total variation based image recovery algorithms have highcomputational complexity, so introduce gradient projection(GP) method to solve TVbased image processing. This method not only has a very fast computational rate but a good recovery while reduces the continuous distributed Gaussian noise. Howeverwhen it’s utilized in removing salt&pepper noise, it can’t receive a desirable effectbut brings new noise in. Considering that median filtering could efficiently removesalt&pepper noise and many actual images contains mixed noise, so I combine thetwo methods together and obtain a new method: with GP removing Gaussian noisefirst, then median filtering reducing salt&pepper subsequently. This series method isproved very efficiently in removing compound noise. Then, I use GP and IST methodfor blurring image which corrupted by noise and the method could get a very goodreconstruction.