Study On The Reconstruction Algorithm Of Two-dimensional Non-uniform Sampling Signal Based On Compressive Sensing

With the growing demand for information, the pressure of mass data sampling,transmission and storage is getting bigger, the traditional Nyquist sampling theoremencountered great challenges. Compressive Sensing which is developed in recent yearsusing the sparse feature of the signal can reconstruct the original signal by a fewmeasurements, and is showing great advantages and development potential. Furthermore,In the signaling system, due to the influence of various factors, it is difficult to realizeuniform sampling signal in a real sense. the situation of non-uniform sampling iswidespread. In this paper, based on the theory of compressed sensing, the two-dimensionalnon-uniform sampling signal (two-dimensional seismic signal and digital image, forexample) reconstruction algorithm is researched.The main research work in this paper is as follows:(1)Two-dimensional seismic signal reconstruction based on K-SVD dictionarylearning within compressive sensing framework.The seismic signal often appears incomplete or irregular problems due to the influenceof sampling cost and environmental factors in seismic exploration. Considering the existingseismic signal reconstruction methods based on Compressive Sensing are using a fixedbasis functions, and can not construct the transform base according to a given seismicsignal adaptively, this paper presents an algorithm of seismic signal reconstruction based onK-SVD dictionary-learning within compressive sensing framework. The basic idea is totrain an over complete dictionary by K-SVD dictionary learning based on a large numberof seismic signal samples firstly, then introduce the sampling matrix of seismic signal as ameasurement matrix, and finally reconstruct the seismic signal through the regularizedorthogonal matching pursuit algorithm (ROMP) in the reconstruction phase. From theexperiment of the synthetic seismic signal and real marine seismic data, we verified thefeasibility and efficiency of the method.(2)Sparsity adaptive algorithm for image inpainting based on compressive sensingGreedy algorithm has a lower computational complexity and higher reconstructionefficiency, but the typical algorithms of greedy algorithm such as MP, OMP, ROMP and soon all need the sparse degree of the known signal. To solve this problem, this paper proposes sparsity adaptive regularized orthogonal matching pursuit algorithm (SA-ROMP).By introducing the logistic regression function, SA-ROMP algorithm select atoms in theprocess of each iteration adaptively, is more flexible to determine the atomic candidate set,and can be very good to finish the damaged image restoration under the circumstances ofsparse degree is unknown. A comparison based on experimental results shows the proposedalgorithm is feasible and better than other similar algorithms.(3)Layered image restoration based on morphological component analysis (MCA)under the Compressive Sensing FrameworkAccording to the principles of visual, natural images can be decomposed into thevisual structure and texture parts. The current image inpainting algorithm, mostly to repairthe damaged image as a whole, and not not make full use of the structure and textureinformation, thus would inevitably cause some features missing.In this regard, the paperadded the idea of decomposition in the inpainting of damaged images under the frameworkof Compressive Sensing. The specific idea is to decompose the image by MCA algorithmfirst, and then based on the characteristics of structure and texture parts, the method ofCDD model is adopted to repair the image structure part and the texture part is repaired byBregman iterative algorithm. Finally merge the two parts results. Verified by experiment,adding the idea of decomposition, the image restoration effect increased.