本文選題：壓縮感知 + 觀測矩陣��； 參考：《南京郵電大學(xué)》2017年碩士論文

【摘要】：壓縮感知是一種新興起的采樣理論,信號在采樣的同時完成了壓縮,打破了的傳統(tǒng)Nyquist采樣定理。壓縮感知充分依據(jù)信號是可稀疏的,利用非自適應(yīng)線性投影來盡量保留原始信號的信息,并利用數(shù)值凸優(yōu)化精確解析重構(gòu)信號。本文主要針對壓縮感知中觀測矩陣優(yōu)化與重構(gòu)算法設(shè)計這兩部分做了以下研究:1.介紹了梯度下降法與QR分解原理,提出一種新的觀測矩陣優(yōu)化。并對它進行實驗仿真,與現(xiàn)有的幾種矩陣優(yōu)化方法對比分析,此優(yōu)化方法在提高峰值信噪比和重構(gòu)穩(wěn)定性方面具有較好的效果。2.具體介紹了增大矩陣列獨立性的矩陣分解原理,并利用梯度下降法降低觀測矩陣同稀疏矩陣之間的相關(guān)性,將二者相結(jié)合進一步改進觀測矩陣。對比仿真實驗結(jié)果表明,新矩陣具有較好的重構(gòu)性能。3.提出了一種將改進的觀測矩陣與共軛梯度法相結(jié)合的算法。針對于共軛梯度重構(gòu)算法,優(yōu)化其觀測矩陣,得到新的重構(gòu)算法,此算法保留了觀測矩陣優(yōu)化OMP算法的穩(wěn)定性和魯棒性,同時又具備共軛梯度算法的嚴(yán)謹(jǐn)性。實驗仿真表明,改進后觀測矩陣的共軛梯度算法的重構(gòu)時間大大減少,并證實了其可行性與優(yōu)越性。
[Abstract]:Compression sensing is a new sampling theory. The signal is compressed at the same time, which breaks the traditional Nyquist sampling theorem. Compression sensing is based on the sparsity of the signal, the non-adaptive linear projection is used to keep the original signal information as much as possible, and the numerical convexity optimization is used to accurately analyze the reconstructed signal. In this paper, we focus on the optimization and reconstruction algorithm design of observation matrix in compressed sensing, and do the following research: 1. The gradient descent method and QR decomposition principle are introduced, and a new optimization of observation matrix is proposed. The simulation results are compared with the existing matrix optimization methods. The results show that this optimization method can improve the PSNR and the reconstruction stability. 2. The principle of matrix decomposition to increase the independence of matrix column is introduced in detail, and the correlation between observation matrix and sparse matrix is reduced by gradient descent method, and the observation matrix is further improved by combining the two methods. The simulation results show that the new matrix has good reconstruction performance. 3. An algorithm combining the improved observation matrix with the conjugate gradient method is proposed. For the conjugate gradient reconstruction algorithm, the observation matrix is optimized, and a new reconstruction algorithm is obtained. This algorithm preserves the stability and robustness of the observation matrix optimization OMP algorithm and has the preciseness of the conjugate gradient algorithm at the same time. The experimental results show that the reconstruction time of the conjugate gradient algorithm of the improved observation matrix is greatly reduced and the feasibility and superiority of the algorithm are verified.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.7

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本文編號：2045580