本文選題：壓縮感知 + 測(cè)量矩陣��； 參考：《湖南師范大學(xué)》2014年碩士論文

【摘要】：用遠(yuǎn)低于尼奎斯特頻率的采樣速率來(lái)收集信號(hào),并在接收端通過(guò)相應(yīng)的恢復(fù)算法完成對(duì)原始信號(hào)精確重構(gòu)的壓縮感知作為一個(gè)全新的信息獲取及處理的理論框架,打破了傳統(tǒng)的尼奎斯特香農(nóng)采樣理論,成為信號(hào)處理各個(gè)領(lǐng)域的熱點(diǎn)。 本文在國(guó)內(nèi)外研究的基礎(chǔ)上,從分析壓縮感知理論的基本原理出發(fā),對(duì)基于壓縮感知的圖像采集及重構(gòu)算法進(jìn)行了詳細(xì)研究。從構(gòu)造合適的確定性測(cè)量矩陣以及提高圖像重構(gòu)算法精度等方面入手,重點(diǎn)研究了常用的測(cè)量矩陣、貪婪追蹤算法等內(nèi)容。論文主要貢獻(xiàn)有以下幾個(gè)方面： 第一,給出了基于低密度奇偶校驗(yàn)矩陣的確定性測(cè)量矩陣。針對(duì)目前常用的隨機(jī)測(cè)量矩陣計(jì)算復(fù)雜度高、需要的存儲(chǔ)空間大以及硬件上不易實(shí)現(xiàn)的缺點(diǎn),考慮低密度奇偶檢查碼編解碼與壓縮感知理論之間的相似性,提出將Gallager構(gòu)造的階梯校驗(yàn)矩陣作為測(cè)量矩陣應(yīng)用于壓縮感知。此外,結(jié)合PEG算法和準(zhǔn)循環(huán)構(gòu)造法,構(gòu)造一種基于PEG算法的準(zhǔn)循環(huán)測(cè)量矩陣。兩種新的測(cè)量矩陣在相關(guān)性和Gram矩陣非對(duì)角線(xiàn)上最大元素值幾個(gè)衡量參數(shù)上都要優(yōu)于現(xiàn)有的常用測(cè)量矩陣,需要的存儲(chǔ)空間小,便于硬件的實(shí)現(xiàn)。 第二,給出了一種自適應(yīng)前瞻子空間追蹤算法。該算法針對(duì)子空間追蹤算法每次迭代固定的引入內(nèi)積最大的K個(gè)原子加入候選集所引起的誤差,引進(jìn)前瞻策略和自適應(yīng)選擇步長(zhǎng)的方法,既保證了提高信號(hào)重構(gòu)的精度又平衡了重構(gòu)所需的時(shí)間。 通過(guò)Matlab軟件對(duì)上述提出的測(cè)量矩陣以及算法進(jìn)行仿真實(shí)驗(yàn),分析實(shí)驗(yàn)結(jié)果,驗(yàn)證了提出來(lái)的測(cè)量矩陣在性能上優(yōu)于現(xiàn)在常用的測(cè)量矩陣,改進(jìn)的重構(gòu)算法相比其他的貪婪追蹤算法在一維信號(hào)和二維圖像重構(gòu)上也具有一定的優(yōu)越性。
[Abstract]:The signal is collected at a rate far below the Nyquist frequency, and the compression perception of the accurate reconstruction of the original signal is accomplished by the corresponding recovery algorithm at the receiving end as a new theoretical framework for information acquisition and processing. It breaks the traditional Nyquist Shannon sampling theory and becomes a hot spot in all fields of signal processing. Based on the research at home and abroad, the image acquisition and reconstruction algorithm based on compression perception is studied in detail, based on the analysis of the basic principle of compression perception theory. From the aspects of constructing suitable deterministic measurement matrix and improving the precision of image reconstruction algorithm, the common measurement matrix and greedy tracking algorithm are studied emphatically. The main contributions of the thesis are as follows: First, the deterministic measurement matrix based on low density parity check matrix is given. In view of the high computational complexity, the large storage space and the difficulty in hardware implementation of the random measurement matrix, the similarity between the low density parity check code coding and decoding and the compression sensing theory is considered. The step check matrix constructed by Gallager is applied to compression sensing as a measurement matrix. In addition, combined with PEG algorithm and quasi-cyclic construction method, a quasi-cyclic measurement matrix based on PEG algorithm is constructed. The two new measurement matrices are superior to the existing measurement matrices in terms of the correlation and the maximum element value on the non-diagonal Gram matrix. The storage space is small and the hardware is easy to implement. Secondly, an adaptive prospective subspace tracking algorithm is presented. Aiming at the errors caused by the introduction of K atoms with the largest inner product into the candidate set in each iteration of the subspace tracking algorithm, the forward looking strategy and the adaptive selection of step size are introduced. It can not only improve the precision of signal reconstruction, but also balance the time needed for reconstruction. The proposed measurement matrix and algorithm are simulated by Matlab software, and the experimental results are analyzed. The performance of the proposed measurement matrix is better than that of the commonly used measurement matrix. Compared with other greedy tracking algorithms, the improved reconstruction algorithm also has some advantages in one dimensional and two dimensional image reconstruction.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TN911.73

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