| In the signal processing, Nyquist sampling theorem must be satisfied in the sampling process. However, as the modern bandwidth becomes more and more wider, the sampling theorem brings more and more challenge to the hardware. The compressive sensing theory is an important milestone in the signal processing field, it combines sampling process with compressing process, succeed in breaking the constraints of the sampling theorem.The main content in this paper is researching the reconstruction algorithm in compressive sensing. The algorithm for researching is based on the Orthogonal Matching Pursuit(OMP)algorithm. In this paper, we firstly introduce the basic algorithm-OMP algorithm. After that, Subspace Pursuit(SP)algorithm, Regularized Orthogonal Matching Pursuit(ROMP)algorithm, Sparsity Adaptive Matching Pursuit(SAMP)algorithm are introduced. These algorithms improve the OMP algorithm in different aspects. However, there is still space for improving the effect of the improved algorithm, two new reconstruction algorithms are presented in this paper: Exponential Sparsity Adaptive Matching Pursuit (ESAMP) algorithm, Exponential adaptive Regularized Orthogonal Matching Pursui(tEaROMP) algorithm. The new algorithms add adaptive operator to SAMP algorithm and ROMP algorithm, the adaptive operator makes the sparsity change adaptively as the number of iterations of algorithm increases. Considering that the signal for reconstruction algorithm is always very sparse, the sparsity of the new algorithm increases exponentially, which can be explained intuitively as: searching in small sparsity K is detailed and in big sparsity K is rough.In this paper, we experiment on many actual images, and make comparison with the original algorithm. The results show: the new algorithm does better in image reconstruction than the original algorithm, and the adaptive algorithm does not need to know the sparsity in advance, the algorithm can be used more universally, and reduce the number of iterations. |
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