基于過完備字典的非凸壓縮感知理論與方法研究
發(fā)布時間：2018-07-26 18:29
【摘要】：壓縮感知是一種全新的信號獲取和處理框架,其理論和技術(shù)的發(fā)展將對數(shù)字信號的獲取方式,分析技術(shù)和處理方法等研究領(lǐng)域及相關(guān)應(yīng)用領(lǐng)域產(chǎn)生深遠的影響。目前,壓縮感知正從理論研究向?qū)嶋H的信號應(yīng)用領(lǐng)域發(fā)展:處理的數(shù)據(jù)對象從具有簡單的理想稀疏性信號轉(zhuǎn)向廣泛的具有復(fù)雜低維結(jié)構(gòu)的實際信號;信號的稀疏表示從基于正交基和框架發(fā)展為基于結(jié)構(gòu)化的冗余字典;研究重點從理論研究發(fā)展為對應(yīng)用中實際信號的重構(gòu)和處理。其中,根據(jù)應(yīng)用需求建立結(jié)構(gòu)化重構(gòu)模型以及高效的重構(gòu)算法是壓縮感知從理論走向?qū)嵺`中最重要的環(huán)節(jié),也是壓縮感知應(yīng)用研究的熱點。本論文工作中,建立了分塊策略下的基于過完備字典的圖像非凸壓縮感知框架,其中,對圖像進行分塊壓縮觀測,即對圖像的每個大小相等的圖像塊使用相同的隨機觀測方式;構(gòu)造了Ridgelet過完備字典,獲得對任意圖像塊的稀疏表示;挖掘和利用圖像塊在Ridgelet過完備字典中的稀疏性和結(jié)構(gòu)稀疏先驗,設(shè)計了從圖像塊的壓縮觀測中獲得圖像準確估計的重構(gòu)模型。在此框架下,針對壓縮感知重構(gòu)的本源問題,即0l范數(shù)約束的非凸優(yōu)化問題,我們提出了基于自然計算優(yōu)化算法和協(xié)同優(yōu)化的重構(gòu)思路,建立了能夠有效求解包含了非凸稀疏先驗以及多種結(jié)構(gòu)先驗約束的圖像重構(gòu)方法。論文的主要工作包括:(1)為了獲得全局尋優(yōu)意義下的非凸壓縮感知重構(gòu),提出了基于自然計算優(yōu)化算法的兩階段重構(gòu)框架。在該框架的第一階段,設(shè)計了一種遺傳算法來獲得一類圖像塊在方向上的最優(yōu)原子組合;第二階段在第一階段結(jié)果的基礎(chǔ)上,設(shè)計了一種克隆選擇算法來搜索自適應(yīng)于每個圖像塊的子字典,并獲得每個圖像塊在尺度和位移等參數(shù)上的更優(yōu)原子組合。該框架采用全局尋優(yōu)的進化搜索策略,通過靈活多樣的進化策略設(shè)計來實現(xiàn)零范數(shù)和圖像結(jié)構(gòu)先驗約束下的圖像分塊壓縮感知重構(gòu)。該工作是自然計算優(yōu)化方法在非凸壓縮感知重構(gòu)中的成功應(yīng)用嘗試,能夠獲得對圖像較好的重構(gòu)估計。(2)考慮到基于進化搜索策略的重構(gòu)方法存在重構(gòu)速度較慢的問題,提出了基于過完備字典的協(xié)同壓縮感知重構(gòu),其主要思想是用匹配追蹤方法的局部搜索和交迭優(yōu)化策略代替進化搜索中的全局搜索策略。該方法利用了圖像的自相似特性,設(shè)計了兩種協(xié)同重構(gòu)方式,用于在局部和非局部相似的圖像塊間進行重構(gòu)信息的傳遞和交換。第一種協(xié)同方式利用一組相似圖像塊的觀測向量來重構(gòu)單個圖像塊,第二種協(xié)同方式則利用一組圖像塊的估計值來獲得對單個圖像塊的更優(yōu)估計。實驗結(jié)果表明,所提出的方法可以有效減少采用基于進化搜索策略的重構(gòu)方法的運行時間,在性能上超過了經(jīng)典匹配追蹤算法。(3)為了獲得對圖像塊局部結(jié)構(gòu)的更準確估計,并提升已有協(xié)同重構(gòu)方法,提出了一種幾何結(jié)構(gòu)指導(dǎo)的協(xié)同重構(gòu)方法。該方法根據(jù)過完備字典中原子結(jié)構(gòu)與圖像塊結(jié)構(gòu)的匹配關(guān)系,對圖像塊在字典中的稀疏表示系數(shù)施加塊稀疏結(jié)構(gòu)約束,并將這些約束與協(xié)同重構(gòu)機制結(jié)合,分別設(shè)計了針對光滑,單方向和隨機結(jié)構(gòu)圖像塊的協(xié)同重構(gòu)模式和重構(gòu)策略。與已有的協(xié)同重構(gòu)方法相比,結(jié)合了幾何結(jié)構(gòu)先驗的協(xié)同重構(gòu)方法能夠有效改善圖像局部結(jié)構(gòu)估計,并在重構(gòu)精度和速度上都有所提升。(4)為了結(jié)合和利用圖像塊基于過完備字典的方向結(jié)構(gòu)先驗來獲得對圖像及其局部結(jié)構(gòu)的準確重構(gòu),提出了基于方向指導(dǎo)的字典及進化搜索的重構(gòu)策略。其中設(shè)計和提出了一種利用Ridgelet過完備字典根據(jù)圖像塊的壓縮觀測判定圖像塊結(jié)構(gòu)類型的解析方法,將圖像塊判定為光滑,單方向和多方向塊中的一種,并對單方向和多方向塊的方向結(jié)構(gòu)進行估計。根據(jù)對圖像塊的結(jié)構(gòu)估計,我們?yōu)楣饣蛦畏较驁D像塊構(gòu)造了稀疏子字典,并設(shè)計了方向指導(dǎo)的進化搜索重構(gòu)策略。該重構(gòu)策略中,對光滑圖像塊采用單階段的進化重構(gòu)策略;對單方向和多方向圖像塊首先基于方向指導(dǎo)的結(jié)構(gòu)稀疏模型進行重構(gòu),再采用進化搜索策略進行再次優(yōu)化估計。與已有的兩階段進化重構(gòu)策略相比,本重構(gòu)策略能夠獲得更準確的方向結(jié)構(gòu)估計,以及更高的重構(gòu)速度。通過本工作,展示了基于進化搜索的優(yōu)化方法在具有非凸稀疏約束及其他結(jié)構(gòu)先驗共同約束的優(yōu)化問題中的應(yīng)用前景。
[Abstract]:Compressed sensing is a new framework for signal acquisition and processing. The development of its theory and technology will have a profound impact on the research fields of digital signal acquisition, analysis technology and processing methods and related applications. At present, compression perception is developing from theoretical research to real signal application field: data object processing. From simple ideal sparsity signals to a wide range of practical signals with complex and low dimensional structures; sparse representations of signals are developed from based on orthogonal bases and frameworks to structured redundant dictionaries; the focus of research is developed from theoretical research to the reconstruction and processing of practical signals in applications. The most important part of compression perception from theory to practice is the most important part of compression perception from theory to practice, and also a hot spot in compressed sensing application research. In this paper, an image non convex compression frame based on overcomplete dictionary based on partitioned strategy is established, in which the image is divided into block compression observation, that is, to the image Each image block with equal size uses the same random observation method; constructs the Ridgelet overcomplete dictionary to obtain the sparse representation of any image block, and uses the sparsity and the sparse priori in the Ridgelet overcomplete dictionary to excavate and make use of the image block in the overcomplete dictionary of the image. In this framework, in view of the source problem of compressed sensing reconstruction, that is, the non convex optimization problem of 0l norm constraint, we propose a reconstruction idea based on the natural computing optimization algorithm and the cooperative optimization, and establish an image reconstruction method which can effectively solve the non convex sparse prior and a variety of structure prior constraints. The work includes: (1) in order to obtain the non convex compression perception reconstruction under the global optimization, a two phase reconstruction framework based on the natural computing optimization algorithm is proposed. In the first stage of the framework, a genetic algorithm is designed to obtain the optimal combination of a class of image blocks in the direction; the second stage is based on the first stage result. A clonal selection algorithm is designed to search the sub dictionaries adaptive to each image block and obtain better atomic combinations of each image block on the parameters of scale and displacement. The framework uses a global optimization evolutionary search strategy to achieve zero norm and image structure prior constraints by a flexible and diverse evolutionary strategy design. This work is a successful application of natural computing optimization method in non convex compression sensing reconstruction, which can obtain better reconstruction estimation for images. (2) considering the problem of slow reconstruction in the reconstruction method based on evolutionary search strategy, a cooperative compression perception based on overcomplete dictionary is proposed. The main idea is to replace the global search strategy in the evolutionary search with the local search and overlapping optimization strategy of matching pursuit method. The method uses the self similarity of the image, and designs two cooperative reconfiguration methods for the transfer and exchange of the reconstruction information between the local and non local similar image blocks. In the same way, an observation vector of a group of similar image blocks is used to reconstruct a single image block. The second cooperative methods use an estimated value of a block of image blocks to obtain a better estimate of a single image block. The experimental results show that the proposed method can effectively reduce the running time of the reconfiguration method based on the evolutionary search strategy. 3. (3) in order to obtain more accurate estimation of the local structure of the image block, and to improve the existing cooperative reconfiguration method, a collaborative reconstruction method guided by geometric structure is proposed. The representation coefficient applies the block sparse structure constraint, and combines these constraints with the cooperative reconfiguration mechanism, designs the cooperative reconstruction mode and reconfiguration strategy for smooth, single direction and random structure image blocks respectively. Compared with the existing cooperative reconstruction method, the cooperative reconstruction method combining the geometric structure first test can effectively improve the image part. The structure estimation and the reconstruction precision and speed have been improved. (4) in order to combine and utilize the image block based on the direction structure prior to the overcomplete dictionary, the accurate reconstruction of the image and its local structure is obtained. A dictionary based on direction guidance and the reconstruction strategy of evolutionary search are proposed, in which a kind of use of Ridgelet is designed and proposed. An overcomplete dictionary determines the structure type of the block according to the compression observation of the image block. The image block is determined as one of the smooth, single and multi direction blocks, and the direction structure of the single direction and multi direction block is estimated. According to the structure estimation of the image block, we construct the sparsity for the smooth and single direction image blocks. An evolutionary search reconfiguration strategy directed by direction is designed. In this reconfiguration strategy, a single stage evolutionary reconfiguration strategy is adopted for smooth image blocks; a single directional and multi direction image block is restructured in the first direction based structural sparse model, and then the evolutionary search strategy is used for the reoptimization estimation. The two phase of the reconfiguration is made with the existing evolutionary search strategy. Compared with the evolutionary reconstruction strategy, this reconfiguration strategy can obtain more accurate direction structure estimation and higher reconstruction speed. Through this work, the optimization method based on evolutionary search is shown to be applied in the optimization problem with non convex sparse constraints and other structural priori constraints.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.41
本文編號：2146917
[Abstract]:Compressed sensing is a new framework for signal acquisition and processing. The development of its theory and technology will have a profound impact on the research fields of digital signal acquisition, analysis technology and processing methods and related applications. At present, compression perception is developing from theoretical research to real signal application field: data object processing. From simple ideal sparsity signals to a wide range of practical signals with complex and low dimensional structures; sparse representations of signals are developed from based on orthogonal bases and frameworks to structured redundant dictionaries; the focus of research is developed from theoretical research to the reconstruction and processing of practical signals in applications. The most important part of compression perception from theory to practice is the most important part of compression perception from theory to practice, and also a hot spot in compressed sensing application research. In this paper, an image non convex compression frame based on overcomplete dictionary based on partitioned strategy is established, in which the image is divided into block compression observation, that is, to the image Each image block with equal size uses the same random observation method; constructs the Ridgelet overcomplete dictionary to obtain the sparse representation of any image block, and uses the sparsity and the sparse priori in the Ridgelet overcomplete dictionary to excavate and make use of the image block in the overcomplete dictionary of the image. In this framework, in view of the source problem of compressed sensing reconstruction, that is, the non convex optimization problem of 0l norm constraint, we propose a reconstruction idea based on the natural computing optimization algorithm and the cooperative optimization, and establish an image reconstruction method which can effectively solve the non convex sparse prior and a variety of structure prior constraints. The work includes: (1) in order to obtain the non convex compression perception reconstruction under the global optimization, a two phase reconstruction framework based on the natural computing optimization algorithm is proposed. In the first stage of the framework, a genetic algorithm is designed to obtain the optimal combination of a class of image blocks in the direction; the second stage is based on the first stage result. A clonal selection algorithm is designed to search the sub dictionaries adaptive to each image block and obtain better atomic combinations of each image block on the parameters of scale and displacement. The framework uses a global optimization evolutionary search strategy to achieve zero norm and image structure prior constraints by a flexible and diverse evolutionary strategy design. This work is a successful application of natural computing optimization method in non convex compression sensing reconstruction, which can obtain better reconstruction estimation for images. (2) considering the problem of slow reconstruction in the reconstruction method based on evolutionary search strategy, a cooperative compression perception based on overcomplete dictionary is proposed. The main idea is to replace the global search strategy in the evolutionary search with the local search and overlapping optimization strategy of matching pursuit method. The method uses the self similarity of the image, and designs two cooperative reconfiguration methods for the transfer and exchange of the reconstruction information between the local and non local similar image blocks. In the same way, an observation vector of a group of similar image blocks is used to reconstruct a single image block. The second cooperative methods use an estimated value of a block of image blocks to obtain a better estimate of a single image block. The experimental results show that the proposed method can effectively reduce the running time of the reconfiguration method based on the evolutionary search strategy. 3. (3) in order to obtain more accurate estimation of the local structure of the image block, and to improve the existing cooperative reconfiguration method, a collaborative reconstruction method guided by geometric structure is proposed. The representation coefficient applies the block sparse structure constraint, and combines these constraints with the cooperative reconfiguration mechanism, designs the cooperative reconstruction mode and reconfiguration strategy for smooth, single direction and random structure image blocks respectively. Compared with the existing cooperative reconstruction method, the cooperative reconstruction method combining the geometric structure first test can effectively improve the image part. The structure estimation and the reconstruction precision and speed have been improved. (4) in order to combine and utilize the image block based on the direction structure prior to the overcomplete dictionary, the accurate reconstruction of the image and its local structure is obtained. A dictionary based on direction guidance and the reconstruction strategy of evolutionary search are proposed, in which a kind of use of Ridgelet is designed and proposed. An overcomplete dictionary determines the structure type of the block according to the compression observation of the image block. The image block is determined as one of the smooth, single and multi direction blocks, and the direction structure of the single direction and multi direction block is estimated. According to the structure estimation of the image block, we construct the sparsity for the smooth and single direction image blocks. An evolutionary search reconfiguration strategy directed by direction is designed. In this reconfiguration strategy, a single stage evolutionary reconfiguration strategy is adopted for smooth image blocks; a single directional and multi direction image block is restructured in the first direction based structural sparse model, and then the evolutionary search strategy is used for the reoptimization estimation. The two phase of the reconfiguration is made with the existing evolutionary search strategy. Compared with the evolutionary reconstruction strategy, this reconfiguration strategy can obtain more accurate direction structure estimation and higher reconstruction speed. Through this work, the optimization method based on evolutionary search is shown to be applied in the optimization problem with non convex sparse constraints and other structural priori constraints.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.41
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