基于压缩感知的图像编解码方法研究
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摘要
视觉传感器通常以远超出有效维度对图像信号采样，从而导致了存储和传输的巨大压力。压缩感知理论表明：在某个变换域下稀疏的信号，可以利用优化方法由少量观测数据稀疏重建。这种非自适应的压缩采样将信号中包含的信息凝聚在少量的观测数据上，大幅度地降低了精确重建原始信号所需要的采样数目。压缩感知理论改变了图像信息的获取、传输和识别方式，在图像处理领域获得了巨大的成功。
在传统压缩感知框架下，通常将高维的图像数据转化为一维向量进行观测，这就破坏了图像数据的高维结构特性，降低了图像信息的获取能力；并且通常假设噪声是均匀的且具有相同分布特性，导致了重建过程的鲁棒性能低下；忽略图像信号在稀疏基下呈现的结构特性，影响了图像重建质量。本文围绕上述问题展开研究，以压缩感知理论为指导，建立了图像信号的二维观测方法，提出了均衡化量化噪声重建模型和小波域分组稀疏模型。论文的主要工作集中在如下几个方面：
第一，针对现有基于一维的观测无法有效获取图像的二维相关信息的问题，本文提出了图像信号的二维观测方法。通过研究混合编码框架下变换与压缩感知理论框架下观测之间的联系，给出了将图像视频信号的二维变换等效为压缩感知观测的方法，实现了压缩感知方法和传统变换方法的融合，该方法有效地捕捉到信号各个维度上的不同特性，显著地提高了观测过程对图像信号的信息获取能力。实验结果表明，这一方法能有效提升图像的压缩感知重建效果。
第二，针对现有图像编解码方法中非一致量化带来的噪声问题，利用压缩感知的重建理论，提出了一种均衡化量化噪声重建模型。通过统计不同量化噪声情形下不同图像的最优误差限，建立了量化噪声水平和优化重建误差参数之间的模型。由该模型指导，针对非一致量化器推导了一个新的均衡化误差约束来代替原有的量化噪声误差约束。实验结果表明，均衡化量化噪声模型对非一致量化下的噪声估计有良好效果，显著提升了图像的重建质量。
第三，小波变换是压缩感知重建过程中常用的稀疏基，针对小波域最低频承载图像能量和高频子带表达图像结构这一特性,提出一类分离式分组方法，建立了基于小波域能量结构特性分组稀疏重建模型；同时利用小波域的零树特性，提出一类交叠式分组方法，建立了基于小波域零树结构的分组稀疏重建模型。上述重建模型较为复杂，为此利用算子分裂法和Proximal方法等优化技术，基于上述两种模型，给出了高效的求解算法。实验结果表明本文所提出的基于分组稀疏的信号重建模型能够较大幅度提高图像主客观质量。
The vision sensors usually sample far beyond the effective dimension of theimage signal, leading to in huge pressure the storage and transmission. CompressiveSensing (CS) provides an efficient way to acquire and reconstruct sparse signals froma limited number of linear sub-Nyquist random measurements. Such non-adaptivecompression information included in the signal samples will be collected on a smallnumber of observation data, greatly reduce the number of samples required by theaccurate reconstruction of the original signal. CS changes the image informationacquisition, transmission, and identification and gets huge success in the field ofimage processing.
In traditional compressive sensing codec frame,2D images signals usually arerecast to1D vector in the observation procession which leads to lose the highdimensional structure characteristic of image data. In reconstruction procession,traditional compressive sensing codec frame usually ignores different structurecharacters of different image signal sparse bases and cannot robust recovery imagesfrom noise observation. This paper focus on these issues, proposes2D observationmethod for image signals, group sparse model for fitting sparse bases and equalizationquantization noise model for the non-uniform quantization.The main researchfocusing on the following aspects:
1．For existing one-dimensional observations can not effectively get two-dimensionalinformation of images, this paper presents the method that takes2D CS observation.By studing relationship between the transform of the hybrid coding framework andCS observation, this paper presents the method that takes2D transform of imagessignal equivalent to CS observation and establishes images two dimensional tensorobserving model. This model catches different character of different dimensions ofimages, and improves efficiency the of observation process. The experimental resultsshow that this method can effectively improve the quality of the compressed sensingreconstruction.
2. This paper proposes an error estimate method based on equalization andquantization noise model for image codec. Based on sparse constraint, establishes amodel between the quantization noise level and the optimization of reconstructionerror parameters. Due to the robust character of CS, it can upgrade the quality of reconstruction when error has been estimated accurately. With designed equalizationmatrix, a new norm constraint which can enhance the quality of CS recoverysignificantly has been shown. And experimental evidence exhibits more gains over CSreconstruction without error estimation.
3. The wavelet transform is commonly used sparse basis in compressive sensingreconstruction. Due to wavelet transform lowest frequency coefficients take mostenergy of image while high frequency coefficients are sparse and take some importantvision information, this paper proposes a separeated grouping model based on energyfeature of wavelet coefficents; for wavelet coefficients are commonly represented bytree, this paper presents an overlapped grouping model based on wavelet zerotree.These models are complex and the corresponding algorithms based on compositesplitting and proximal method are employed to approach these group sparse models.Experimental results show that proposed models can obviously improve bothobjective and subjective qualities of image recovery.
在传统压缩感知框架下，通常将高维的图像数据转化为一维向量进行观测，这就破坏了图像数据的高维结构特性，降低了图像信息的获取能力；并且通常假设噪声是均匀的且具有相同分布特性，导致了重建过程的鲁棒性能低下；忽略图像信号在稀疏基下呈现的结构特性，影响了图像重建质量。本文围绕上述问题展开研究，以压缩感知理论为指导，建立了图像信号的二维观测方法，提出了均衡化量化噪声重建模型和小波域分组稀疏模型。论文的主要工作集中在如下几个方面：
第一，针对现有基于一维的观测无法有效获取图像的二维相关信息的问题，本文提出了图像信号的二维观测方法。通过研究混合编码框架下变换与压缩感知理论框架下观测之间的联系，给出了将图像视频信号的二维变换等效为压缩感知观测的方法，实现了压缩感知方法和传统变换方法的融合，该方法有效地捕捉到信号各个维度上的不同特性，显著地提高了观测过程对图像信号的信息获取能力。实验结果表明，这一方法能有效提升图像的压缩感知重建效果。
第二，针对现有图像编解码方法中非一致量化带来的噪声问题，利用压缩感知的重建理论，提出了一种均衡化量化噪声重建模型。通过统计不同量化噪声情形下不同图像的最优误差限，建立了量化噪声水平和优化重建误差参数之间的模型。由该模型指导，针对非一致量化器推导了一个新的均衡化误差约束来代替原有的量化噪声误差约束。实验结果表明，均衡化量化噪声模型对非一致量化下的噪声估计有良好效果，显著提升了图像的重建质量。
第三，小波变换是压缩感知重建过程中常用的稀疏基，针对小波域最低频承载图像能量和高频子带表达图像结构这一特性,提出一类分离式分组方法，建立了基于小波域能量结构特性分组稀疏重建模型；同时利用小波域的零树特性，提出一类交叠式分组方法，建立了基于小波域零树结构的分组稀疏重建模型。上述重建模型较为复杂，为此利用算子分裂法和Proximal方法等优化技术，基于上述两种模型，给出了高效的求解算法。实验结果表明本文所提出的基于分组稀疏的信号重建模型能够较大幅度提高图像主客观质量。
The vision sensors usually sample far beyond the effective dimension of theimage signal, leading to in huge pressure the storage and transmission. CompressiveSensing (CS) provides an efficient way to acquire and reconstruct sparse signals froma limited number of linear sub-Nyquist random measurements. Such non-adaptivecompression information included in the signal samples will be collected on a smallnumber of observation data, greatly reduce the number of samples required by theaccurate reconstruction of the original signal. CS changes the image informationacquisition, transmission, and identification and gets huge success in the field ofimage processing.
In traditional compressive sensing codec frame,2D images signals usually arerecast to1D vector in the observation procession which leads to lose the highdimensional structure characteristic of image data. In reconstruction procession,traditional compressive sensing codec frame usually ignores different structurecharacters of different image signal sparse bases and cannot robust recovery imagesfrom noise observation. This paper focus on these issues, proposes2D observationmethod for image signals, group sparse model for fitting sparse bases and equalizationquantization noise model for the non-uniform quantization.The main researchfocusing on the following aspects:
1．For existing one-dimensional observations can not effectively get two-dimensionalinformation of images, this paper presents the method that takes2D CS observation.By studing relationship between the transform of the hybrid coding framework andCS observation, this paper presents the method that takes2D transform of imagessignal equivalent to CS observation and establishes images two dimensional tensorobserving model. This model catches different character of different dimensions ofimages, and improves efficiency the of observation process. The experimental resultsshow that this method can effectively improve the quality of the compressed sensingreconstruction.
2. This paper proposes an error estimate method based on equalization andquantization noise model for image codec. Based on sparse constraint, establishes amodel between the quantization noise level and the optimization of reconstructionerror parameters. Due to the robust character of CS, it can upgrade the quality of reconstruction when error has been estimated accurately. With designed equalizationmatrix, a new norm constraint which can enhance the quality of CS recoverysignificantly has been shown. And experimental evidence exhibits more gains over CSreconstruction without error estimation.
3. The wavelet transform is commonly used sparse basis in compressive sensingreconstruction. Due to wavelet transform lowest frequency coefficients take mostenergy of image while high frequency coefficients are sparse and take some importantvision information, this paper proposes a separeated grouping model based on energyfeature of wavelet coefficents; for wavelet coefficients are commonly represented bytree, this paper presents an overlapped grouping model based on wavelet zerotree.These models are complex and the corresponding algorithms based on compositesplitting and proximal method are employed to approach these group sparse models.Experimental results show that proposed models can obviously improve bothobjective and subjective qualities of image recovery.
引文
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