基于離散Gabor變換的信號稀疏時頻表示
發(fā)布時間：2018-07-25 13:45
【摘要】：離散Gabor變換是一種重要的時頻分析工具,已經(jīng)在數(shù)字信號處理、數(shù)字圖像處理、系統(tǒng)建模中得到廣泛的應用。在過去的十年里,稀疏變換已經(jīng)被證明是一種全新的、有效的數(shù)學工具并成功應用于語音處理、圖像去噪、壓縮感知等工程領(lǐng)域。本文將稀疏變換理論應用于離散Gabor變換,研究了基于離散Gabor變換的信號稀疏時頻表示方法。傳統(tǒng)的離散Gabor變換在過抽樣情況下是冗余的變換,且包含大量的非零變換系數(shù),信號的稀疏表示可利用盡可能少的非零Gabor變換系數(shù)來表示原始信號,所以基于稀疏理論的離散Gabor變換能夠提高Gabor時頻譜的分辨率和集中度從而使離散Gabor變換更加有效地運用于非平穩(wěn)信號分析和處理。主要研究內(nèi)容和創(chuàng)新成果如下：提出了一種基于離散Gabor變換的信號稀疏時頻表示方法。離散Gabor變換中窗函數(shù)寬度直接決定了Gabor時頻譜的聚集性和時頻分辨率。首先我們利用Gabor時頻譜熵度量確定了信號在離散Gabor變換中最優(yōu)窗函數(shù)的寬度,然后將離散Gabor變換轉(zhuǎn)換成帶有l(wèi)p稀疏約束的凸優(yōu)化方程,最后根據(jù)稀疏模型求出近似解。由于基于l1范數(shù)的稀疏約束模型得到的解往往不夠穩(wěn)定,該模型容易導致解過于稀疏并且破壞解的內(nèi)在結(jié)構(gòu),而使用基于l1-l2混合范數(shù)的稀疏約束模型得到的解具有較好的稀疏性和穩(wěn)定性,因此該模型具有實際的工程應用價值。實驗也表明基于此稀疏約束模型獲得的Gabor時頻譜具有較好的時頻集中度并且在降噪方面具有更好的效果。提出了一種基于多窗離散Gabor變換的信號稀疏時頻表示方法。多窗離散Gabor變換可以克服單窗離散Gabor變換具有固定時頻分辨率的缺點,基于多窗離散Gabor變換的結(jié)構(gòu)化稀疏時頻表示方法可以對信號進行有效的分解和分析。首先將多窗離散Gabor變換轉(zhuǎn)換成帶有混合范數(shù)(lp,q)約束下的凸優(yōu)化方程,然后根據(jù)不同的混合范數(shù)使用相應的軟門限函數(shù),最后使用塊坐標下降法獲得稀疏Gabor系數(shù)。實驗表明所提出的方法能獲得更高精度的時頻譜。提出了一種基于矩陣分解和快速傅里葉變換的對偶窗快速求解算法。由于在稀疏分析中,需要分析窗對應的對偶窗來綜合還原信號,因此研究對偶窗的快速求解算法十分必要。本文提出了一種基于矩陣分解和快速傅里葉變換的對偶窗的快速求解方法。該方法首先根據(jù)離散Gabor變換的完備性條件得到了變換窗的新雙正交關(guān)系式,然后對新雙正交關(guān)系式的線性方程組進行簡化并分解成一定數(shù)量的獨立線性子方程組,每一子方程組可利用快速傅里葉變換求解對偶窗,從而可節(jié)省大量的計算時間,實驗驗證了方法的有效性和快速性。提出了一種基于加權(quán)線性組合分析窗的離散Gabor變換及其權(quán)值求解算法。在傳統(tǒng)的多窗離散Gabor變換中,Gabor組合時頻譜的時頻精度不僅取決于所選擇的分析窗還取決于這些窗的線性組合權(quán)值。本文據(jù)此提出了一種基于加權(quán)線性組合分析窗的離散Gabor變換算法,利用變換系數(shù)稀疏性原則從而將加權(quán)線性組合分析窗的離散Gabor變換轉(zhuǎn)換成帶有l(wèi)1-l2范數(shù)約束下的稀疏方程,進而根據(jù)稀疏變換理論求解出窗函數(shù)的權(quán)值。由于求解窗函數(shù)權(quán)值的迭代過程中需要計算組合分析窗對應的綜合窗序列,所以使用前面提出的對偶窗序列的快速求解算法可以減少運算時間和加快運算速度。實驗表明了所提出的離散Gabor變換的有效性。
[Abstract]:Discrete Gabor transform is an important time frequency analysis tool, which has been widely used in digital signal processing, digital image processing and system modeling. In the past ten years, sparse transformation has been proved to be a new and effective mathematical tool and successfully applied to the engineering fields of speech processing, image denoising, compression perception and so on. In this paper, the sparse transform theory is applied to discrete Gabor transform, and the time-frequency representation method of sparse signal based on discrete Gabor transform is studied. The traditional discrete Gabor transform is redundant in oversampling, and contains a large number of non zero transform coefficients. The sparse representation of the signal can make use of the least non zero Gabor transform coefficients. The discrete Gabor transform based on sparse theory can improve the resolution and concentration of the Gabor spectrum and make the discrete Gabor transform more effectively used for non-stationary signal analysis and processing. The main research content and innovation results are as follows: a sparse time-frequency representation based on discrete Gabor transform is proposed. Method. The width of the window function in the discrete Gabor transform directly determines the aggregation and time frequency resolution of the Gabor spectrum. Firstly, we use the spectrum entropy measure of Gabor to determine the width of the optimal window function in the discrete Gabor transform, and then convert the discrete Gabor transform into a convex optimization equation with LP sparse constraint. Finally, the thinning is based on sparsity. The approximate solution is obtained by the model. The solution obtained by the sparse constraint model based on the L1 norm is often not stable. The model can easily lead to the sparse solution and destroy the inner structure of the solution, and the solution obtained by the sparse constraint model based on the mixed norm of L1-L2 has better sparsity and stability. Therefore, the model has practical engineering. The experiment also shows that the Gabor time spectrum based on this sparse constraint model has better time frequency concentration and better effect on noise reduction. A method of signal sparse time frequency representation based on multi window discrete Gabor transform is proposed. Multi window discrete Gabor transform can be used to overcome single window discrete Gabor transformation. The shortcoming of time-frequency resolution is that the structured sparse time-frequency representation method based on multi window discrete Gabor transform can effectively decompose and analyze the signal. First, the multi window discrete Gabor transform is converted into a convex optimization equation with a mixed norm (LP, q) constraint, and then the corresponding soft threshold function is used according to the different mixed norm, finally, the corresponding soft threshold function is used. Finally, the corresponding soft threshold function is used. The block coordinate descent method is used to obtain the sparse Gabor coefficient. The experiment shows that the proposed method can obtain higher precision time spectrum. A fast algorithm for the dual window based on matrix decomposition and fast Fourier transform is proposed. In the sparse analysis, the pair window corresponding to the window is needed to synthesize the reduction signal, so the dual is studied. In this paper, a fast solution method of dual windows based on matrix decomposition and fast Fourier transform is proposed in this paper. This method first obtains a new biorthogonal formula of the transformation window according to the completeness condition of the discrete Gabor transform, and then simplifies and divides the linear equations of the new double normal cross relation. In order to solve a certain number of independent linear subsets, each subgroup can use fast Fourier transform to solve the dual window, thus saving a lot of calculation time. Experiments verify the effectiveness and speediness of the method. A discrete Gabor transform based on weighted linear combination analysis window and its weight calculation algorithm are proposed. In the multi window discrete Gabor transform, the time frequency accuracy of the frequency spectrum of the Gabor combination depends not only on the selected analysis window but also on the linear combination weights of these windows. In this paper, a discrete Gabor transform algorithm based on the weighted linear combination analysis window is proposed, and the weighted linear combination analysis window is used to make use of the thinning principle of the transform coefficients. The discrete Gabor transform is converted into a sparse equation with L1-L2 norm constraints, and then the weight of the window function is solved according to the sparse transformation theory. The experimental results show the effectiveness of the proposed discrete Gabor transform.
【學位授予單位】：安徽大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TN911.7
，
本文編號：2144005
[Abstract]:Discrete Gabor transform is an important time frequency analysis tool, which has been widely used in digital signal processing, digital image processing and system modeling. In the past ten years, sparse transformation has been proved to be a new and effective mathematical tool and successfully applied to the engineering fields of speech processing, image denoising, compression perception and so on. In this paper, the sparse transform theory is applied to discrete Gabor transform, and the time-frequency representation method of sparse signal based on discrete Gabor transform is studied. The traditional discrete Gabor transform is redundant in oversampling, and contains a large number of non zero transform coefficients. The sparse representation of the signal can make use of the least non zero Gabor transform coefficients. The discrete Gabor transform based on sparse theory can improve the resolution and concentration of the Gabor spectrum and make the discrete Gabor transform more effectively used for non-stationary signal analysis and processing. The main research content and innovation results are as follows: a sparse time-frequency representation based on discrete Gabor transform is proposed. Method. The width of the window function in the discrete Gabor transform directly determines the aggregation and time frequency resolution of the Gabor spectrum. Firstly, we use the spectrum entropy measure of Gabor to determine the width of the optimal window function in the discrete Gabor transform, and then convert the discrete Gabor transform into a convex optimization equation with LP sparse constraint. Finally, the thinning is based on sparsity. The approximate solution is obtained by the model. The solution obtained by the sparse constraint model based on the L1 norm is often not stable. The model can easily lead to the sparse solution and destroy the inner structure of the solution, and the solution obtained by the sparse constraint model based on the mixed norm of L1-L2 has better sparsity and stability. Therefore, the model has practical engineering. The experiment also shows that the Gabor time spectrum based on this sparse constraint model has better time frequency concentration and better effect on noise reduction. A method of signal sparse time frequency representation based on multi window discrete Gabor transform is proposed. Multi window discrete Gabor transform can be used to overcome single window discrete Gabor transformation. The shortcoming of time-frequency resolution is that the structured sparse time-frequency representation method based on multi window discrete Gabor transform can effectively decompose and analyze the signal. First, the multi window discrete Gabor transform is converted into a convex optimization equation with a mixed norm (LP, q) constraint, and then the corresponding soft threshold function is used according to the different mixed norm, finally, the corresponding soft threshold function is used. Finally, the corresponding soft threshold function is used. The block coordinate descent method is used to obtain the sparse Gabor coefficient. The experiment shows that the proposed method can obtain higher precision time spectrum. A fast algorithm for the dual window based on matrix decomposition and fast Fourier transform is proposed. In the sparse analysis, the pair window corresponding to the window is needed to synthesize the reduction signal, so the dual is studied. In this paper, a fast solution method of dual windows based on matrix decomposition and fast Fourier transform is proposed in this paper. This method first obtains a new biorthogonal formula of the transformation window according to the completeness condition of the discrete Gabor transform, and then simplifies and divides the linear equations of the new double normal cross relation. In order to solve a certain number of independent linear subsets, each subgroup can use fast Fourier transform to solve the dual window, thus saving a lot of calculation time. Experiments verify the effectiveness and speediness of the method. A discrete Gabor transform based on weighted linear combination analysis window and its weight calculation algorithm are proposed. In the multi window discrete Gabor transform, the time frequency accuracy of the frequency spectrum of the Gabor combination depends not only on the selected analysis window but also on the linear combination weights of these windows. In this paper, a discrete Gabor transform algorithm based on the weighted linear combination analysis window is proposed, and the weighted linear combination analysis window is used to make use of the thinning principle of the transform coefficients. The discrete Gabor transform is converted into a sparse equation with L1-L2 norm constraints, and then the weight of the window function is solved according to the sparse transformation theory. The experimental results show the effectiveness of the proposed discrete Gabor transform.
【學位授予單位】：安徽大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TN911.7
，
本文編號：2144005
本文鏈接：http://www.wukwdryxk.cn/shoufeilunwen/xxkjbs/2144005.html
最近更新
教材專著
