壓縮感知信號重建算法研究和應用
發(fā)布時間：2018-09-03 06:31
【摘要】：傳統(tǒng)的信號采樣是以Nyquist定理為理論指導,并要求采樣速率達到帶寬的兩倍以上。隨著科技的發(fā)展,在信號采樣的實際應用中,帶寬變得越來越大,傳統(tǒng)的理論采樣已經(jīng)不能滿足人們的要求。一個新的采樣理論應運而生,即壓縮感知理論。它實現(xiàn)了信號采樣過程中的采樣和壓縮的并行操作,將二者合二為一,不需要先得到海量采樣數(shù)據(jù),節(jié)省了大量時間和存儲空間。目前,壓縮感知理論已成為國際上研究的熱點,它在很多領域的實用價值非常高,應用前景十分廣闊。本文對壓縮感知理論進行了系統(tǒng)的介紹,就其中的關鍵環(huán)節(jié):信號的稀疏表示、測量矩陣設計及重建算法作了詳細描述,著重對重建算法中典型的幾種算法作了介紹,并從實驗仿真中比較了它們的性能。而基于光滑0l范數(shù)最小化問題的重建算法在相同或更好精度情況下比其他算法快2至3倍,本文針對光滑0l范數(shù)最小化算法作了以下研究工作:SL0算法選用高斯函數(shù)作為近似估計0l范數(shù)的函數(shù),本文提出了用復合三角函數(shù)近似估計0l范數(shù),函數(shù)圖像顯示了其比已有的高斯函數(shù)更陡峭,因此逼近性能更加優(yōu)良。針對最速下降法的搜索路徑為鋸齒狀和牛頓法在遠離最優(yōu)解時計算較慢的缺點,本文采用最速下降法和牛頓法相結合的方法,對優(yōu)化問題迭代過程中前數(shù)次迭代用最速下降法,之后用阻尼牛頓法。并通過數(shù)值實驗表明了改進算法的有效性,且與其他算法相比,本算法在壓縮圖像重構精度上有明顯提高�；诠饣�0l范數(shù)最小化的NSL0重建算法,針對該算法中用到的阻尼牛頓法在遠離最優(yōu)解時收斂速度慢的缺點,本文采用前數(shù)次迭代用最速下降法,之后用阻尼牛頓法。且在用阻尼牛頓法迭代求解中設計了有效迭代步長,第一次迭代步長由一維精確搜索得到。通過設計迭代步長的更新方案,使得迭代中每一步的計算更為有效,在保證重構精度的同時能夠提升算法的收斂速度。并且在改進算法中加入了支撐集,部分支撐集是用前次迭代得到的稀疏向量來估計的,而后建立了基于支撐集的近似0l范數(shù)最小化問題。通過人工數(shù)據(jù)實驗和機器圖像壓縮重構實驗,表明了改進算法的有效性。
[Abstract]:The traditional signal sampling is guided by the Nyquist theorem, and the sampling rate is required to be more than twice the bandwidth. With the development of science and technology, in the practical application of signal sampling, the bandwidth becomes larger and larger, and the traditional theoretical sampling can no longer meet the needs of people. A new sampling theory emerged as the times require, that is, the theory of compressed perception. It realizes the parallel operation of sampling and compressing in the process of signal sampling. It combines the two operations and saves a lot of time and storage space. At present, the theory of compressed perception has become the focus of international research, it has a very high practical value in many fields, and has a very broad application prospects. In this paper, the theory of compression perception is systematically introduced, and the key links are described in detail, such as the sparse representation of signal, the design of measurement matrix and the reconstruction algorithm, with emphasis on several typical algorithms in the reconstruction algorithm. Their performances are compared by simulation. The reconstruction algorithm based on smooth 0l norm minimization problem is 2 to 3 times faster than other algorithms under the same or better precision. In this paper, the following research work is done for the smooth 0l norm minimization algorithm: SL0 algorithm chooses Gao Si function as the function of approximate estimation of 0l norm. In this paper, a compound trigonometric function is proposed to approximate estimate 0l norm. The function image shows that it is steeper than the existing Gao Si function, so the approximation performance is better. Because the search path of the steepest descent method is sawtooth and Newton's method is slow to calculate far from the optimal solution, this paper adopts the method of the combination of the steepest descent method and Newton's method, and uses the steepest descent method for the first several iterations in the iterative process of the optimization problem. Then the damped Newton method is used. Numerical experiments show the effectiveness of the improved algorithm, and compared with other algorithms, the proposed algorithm can significantly improve the accuracy of image reconstruction. Based on the smooth 0l norm minimization NSL0 reconstruction algorithm, the damped Newton method used in this algorithm has the disadvantage of slow convergence rate when it is far from the optimal solution. In this paper, the first iteration uses the steepest descent method, and then the damped Newton method is used. The effective iteration step size is designed in the iterative solution with damped Newton method. The first iteration step size is obtained by one dimensional exact search. By designing the update scheme of iteration step size, the calculation of each step in the iteration is more efficient, and the convergence speed of the algorithm can be improved while the reconstruction accuracy is guaranteed. The support set is added to the improved algorithm, and the partial support set is estimated by the sparse vector obtained from the previous iteration, and then the approximate 0l norm minimization problem based on the support set is established. The effectiveness of the improved algorithm is demonstrated by artificial data experiments and machine image compression and reconstruction experiments.
【學位授予單位】：西安電子科技大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.7
[Abstract]:The traditional signal sampling is guided by the Nyquist theorem, and the sampling rate is required to be more than twice the bandwidth. With the development of science and technology, in the practical application of signal sampling, the bandwidth becomes larger and larger, and the traditional theoretical sampling can no longer meet the needs of people. A new sampling theory emerged as the times require, that is, the theory of compressed perception. It realizes the parallel operation of sampling and compressing in the process of signal sampling. It combines the two operations and saves a lot of time and storage space. At present, the theory of compressed perception has become the focus of international research, it has a very high practical value in many fields, and has a very broad application prospects. In this paper, the theory of compression perception is systematically introduced, and the key links are described in detail, such as the sparse representation of signal, the design of measurement matrix and the reconstruction algorithm, with emphasis on several typical algorithms in the reconstruction algorithm. Their performances are compared by simulation. The reconstruction algorithm based on smooth 0l norm minimization problem is 2 to 3 times faster than other algorithms under the same or better precision. In this paper, the following research work is done for the smooth 0l norm minimization algorithm: SL0 algorithm chooses Gao Si function as the function of approximate estimation of 0l norm. In this paper, a compound trigonometric function is proposed to approximate estimate 0l norm. The function image shows that it is steeper than the existing Gao Si function, so the approximation performance is better. Because the search path of the steepest descent method is sawtooth and Newton's method is slow to calculate far from the optimal solution, this paper adopts the method of the combination of the steepest descent method and Newton's method, and uses the steepest descent method for the first several iterations in the iterative process of the optimization problem. Then the damped Newton method is used. Numerical experiments show the effectiveness of the improved algorithm, and compared with other algorithms, the proposed algorithm can significantly improve the accuracy of image reconstruction. Based on the smooth 0l norm minimization NSL0 reconstruction algorithm, the damped Newton method used in this algorithm has the disadvantage of slow convergence rate when it is far from the optimal solution. In this paper, the first iteration uses the steepest descent method, and then the damped Newton method is used. The effective iteration step size is designed in the iterative solution with damped Newton method. The first iteration step size is obtained by one dimensional exact search. By designing the update scheme of iteration step size, the calculation of each step in the iteration is more efficient, and the convergence speed of the algorithm can be improved while the reconstruction accuracy is guaranteed. The support set is added to the improved algorithm, and the partial support set is estimated by the sparse vector obtained from the previous iteration, and then the approximate 0l norm minimization problem based on the support set is established. The effectiveness of the improved algorithm is demonstrated by artificial data experiments and machine image compression and reconstruction experiments.
【學位授予單位】：西安電子科技大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.7
【相似文獻】
相關期刊論文 前10條
1 王振天;張麗;邢宇翔;康克軍;;統(tǒng)計重建算法綜述[J];CT理論與應用研究;2007年04期
2 郭威;陳賀新;;一種改進的代數(shù)重建算法及其實現(xiàn)[J];吉林大學學報(工學版);2009年S2期
3 金燕南;趙俊;劉尊鋼;莊天戈;;三源螺旋CT精確重建算法在動態(tài)重建中的應用[J];航天醫(yī)學與醫(yī)學工程;2009年06期
4 杜富瑞;張民;施旭東;安福東;王乾;;基于聲波傳播路徑模擬的溫度場重建算法研究[J];計算機與現(xiàn)代化;2011年09期
5 惠苗;;螺旋錐束精確重建算法優(yōu)化[J];三明學院學報;2012年04期
6 姜永生;于燕燕;;一種適用于小視野的快速精確重建算法[J];東北大學學報(自然科學版);2012年12期
7 鄭健;俞航;蒯多杰;劉兆邦;董月芳;張濤;;多層CT重建算法對比研究[J];CT理論與應用研究;2012年04期
8 白玫;楊雨;嚴漢民;;多排螺旋CT自適應統(tǒng)計迭代重建算法的客觀評價[J];中國醫(yī)學裝備;2013年01期
9 程明淵;賀奇才;胡琴明;陳弟虎;;基于穿越長度權重迭代重建算法的研究[J];中國醫(yī)學物理學雜志;2013年02期
10 閆鑌;韓玉;魏峰;李磊;李建新;;錐束CT超視野成像重建算法綜述[J];CT理論與應用研究;2013年02期
相關會議論文 前10條
1 胡永勝;;重建算法對低劑量肺部CT掃描圖像質(zhì)量和診斷的影響[A];2010中華醫(yī)學會影像技術分會第十八次全國學術大會論文集[C];2010年
2 宋e，
本文編號：2219185
本文鏈接：http://sikaile.net/kejilunwen/wltx/2219185.html
最近更新
教材專著
