方向变换及其在遥感图像压缩中的应用研究
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摘要
随着遥感技术的进步,图像的空间、时间、光谱、辐照分辨率不断提高,以小波等经典变换理论为基础的算法,越来越难以满足高分辨遥感图像大倍率、高保真压缩的需求。经典变换理论的主要缺陷在于,无法稀疏表示遥感图像中特别丰富的几何正则奇异特征。因此,研究适合遥感图像压缩、具有强方向表示能力的新型变换理论,是当前图像压缩算法设计中非常重要的课题。由于压缩对变换冗余度的严格限制,以及实际应用系统对算法实时性的高要求,研究新型方向变换的构造,特别是快速低冗余变换的构造方法,及其高速编码方案,就成为具有挑战性和现实意义的问题。
针对经典压缩变换理论存在的问题,本文从方向特征的稀疏表示着手,深入研究了双树结构多尺度变换、方向提升变换这两类适于图像压缩的方向变换的性质与构造,给出了具有更优方向表示能力和快速实现方案的新型变换算法;并在此基础上,进一步研究了这些新型变换在遥感图像压缩中的应用,特别是针对方向性变换系数的高效编码算法,获得了比现有算法有显著改进的压缩效果。
本文的主要工作包括:
研究了双树变换结构的方向性机理,得到了方向性更优的改进变换算法。(1)针对双树复数小波(DT-CWT)中,基于小波函数的解析性解释方向性存在的不足,通过定义高通滤波器的Hilbert变换对,给出了DT-CWT系数方向性的严格证明。(2)针对原有双树结构中第一层高通滤波器并未构成Hilbert变换对这一缺陷,提出了方向改进双树变换,使得所有变换系数均具有了严格的方向性。(3)将滤波器构成Hilbert变换对作为约束条件,引入到双树滤波器的参数化构造过程中,得到了方向性更优且具有更高消失矩、适于图像压缩的滤波器对。
研究了遥感图像双树变换(DT)系数编码,提出了高效编码方案。针对现有编码方法未充分利用DT系数特性的问题:(1)依据DT系数的方向性,设计了子带方向自适应编码算法。(2)在证明子带不相关性的基础上,给出了适合于DT的失真度计算方法,并进一步提出了基于率失真优化的DT系数编码方案,编码后图像的峰值信噪比(PSNR)较已有算法提高0.1-0.4dB。(3)研究了双树小波域中去噪对压缩的影响,给出了双树小波中噪声的概率密度函数(PDF)的精确表示,与现有PDF相比,更接近于噪声的实际分布,去噪后压缩遥感图像的PSNR可提高0.3dB。
提出了快速方向提升双正交叠式变换(LBT),并给出了相应的低复杂度编码算法。针对现有方向提升计算量过大的缺点:(1)设计了无插值方向模式,提出了可完全重构的快速方向提升LBT,计算量与原有LBT相当。(2)提出了基于裁剪树的全局提升方向优化算法,与现有方向提升块变换(LBT为一种块变换)优化算法相比,计算复杂度由O ( A3 N )降低为O ( AN ),其中A为方向个数,N为像素个数。(3)提出了针对LBT系数特性的量化集合分裂快速编码方法,压缩图像PSNR优于现有方向提升块变换。
本文提出的新型遥感图像变换与编码方法,对于遥感数据的高保真、高速率实时传输具有实用价值。本文中的部分变换及编码技术已经成功应用于航空航天遥感设备的研制中。
With the development of remote sensing, it is becoming more and more difficult to compress remote sensing images with much higher resolution. The traditional transforms used in image compression, such as discrete wavelet transform (DWT), cannot take advantage of geometric regularity in high dimensional signals, which is a central issue to improve compression performance. So, it is critical to develop the transforms with directional selectivity that can represent the anisotropic edges and textures more sparsely. Because remote sensing data must be processed in real time in many cases, the construction of directional transforms with limited redundancy and their fast coding algorithms are the two main challenges.
To get better sparsity, the nature of directions in dual tree (DT) multiscale transform and directional lifting scheme is deeply studied in this thesis. And new fast transforms with improved directional selectivity are constructed. Furthermore, the corresponding efficient codecs are designed and used in remote sensing images compression.
The main contributions in this thesis are as follows.
A new dual-tree structure is proposed, which can represent directional edges and textures in remoting sensing images better. (1) Firstly, the Hilbert transform pair of the high pass filters in DT is defined. Based on the definition, the directional selectivity of DT structure is proved, which is stricter than the explanation based on the analyticity of wavelet functions. (2) Secondly, considering that the filters in the first level DT are not a Hilbert transform pair, a modified DT structure that offers more directional information is proposed. (3) At last, a wavelet pair with better directional selectivity and higher vanishing moments is obtained, by constraining their high pass filters to form a Hilbert transform pair.
A highly efficient codec of DT coefficients is designed based on the proposed DT structure. (1) A direction adaptive context model is developed to reveal the correlation left between adjacent coefficients. (2) The corresponding bands in different trees are proved to be uncorrelated. Using the uncorrelation, a rate-distortion optimization algorithm is proposed and used in DT based compression. Comparing with available DT based compression methods, peak signal-to-noise ratios (PSNR) of our method are 0.1-0.4 dB higher. (3) The influence of denoising on compression in the DT domain is investigated. And a closed-form probability density function (PDF) of noise in DT coefficients is deduced, which approximates the true distribution better comparing with other PDFs now used and gets about 0.3dB coding gain.
A fast directional lifting biorthogonal lapped transform (LBT) is constructed to reduce the computation. (1) The directional mode without interpolation is given and used in directional lifting LBT. It can be performed as efficiently as LBT. (2) An algorithm based on tree pruning is proposed to optimize lifting directions globally. Comparing with the algorithm available, its computation decreases form O ( A3 N ) to O ( AN ), where A is the number of directions and N is the size of the image. (3) A set partition codec is used to code directional lifting LBT coefficients, and the compressed remote sensing images get higher PSNRs.
Our directional transforms and coding algorithms are practical for the high speed and high fidelity transmission of remote sensing images. Some of them have been successfully used in space and aviation remote sensing.
针对经典压缩变换理论存在的问题,本文从方向特征的稀疏表示着手,深入研究了双树结构多尺度变换、方向提升变换这两类适于图像压缩的方向变换的性质与构造,给出了具有更优方向表示能力和快速实现方案的新型变换算法;并在此基础上,进一步研究了这些新型变换在遥感图像压缩中的应用,特别是针对方向性变换系数的高效编码算法,获得了比现有算法有显著改进的压缩效果。
本文的主要工作包括:
研究了双树变换结构的方向性机理,得到了方向性更优的改进变换算法。(1)针对双树复数小波(DT-CWT)中,基于小波函数的解析性解释方向性存在的不足,通过定义高通滤波器的Hilbert变换对,给出了DT-CWT系数方向性的严格证明。(2)针对原有双树结构中第一层高通滤波器并未构成Hilbert变换对这一缺陷,提出了方向改进双树变换,使得所有变换系数均具有了严格的方向性。(3)将滤波器构成Hilbert变换对作为约束条件,引入到双树滤波器的参数化构造过程中,得到了方向性更优且具有更高消失矩、适于图像压缩的滤波器对。
研究了遥感图像双树变换(DT)系数编码,提出了高效编码方案。针对现有编码方法未充分利用DT系数特性的问题:(1)依据DT系数的方向性,设计了子带方向自适应编码算法。(2)在证明子带不相关性的基础上,给出了适合于DT的失真度计算方法,并进一步提出了基于率失真优化的DT系数编码方案,编码后图像的峰值信噪比(PSNR)较已有算法提高0.1-0.4dB。(3)研究了双树小波域中去噪对压缩的影响,给出了双树小波中噪声的概率密度函数(PDF)的精确表示,与现有PDF相比,更接近于噪声的实际分布,去噪后压缩遥感图像的PSNR可提高0.3dB。
提出了快速方向提升双正交叠式变换(LBT),并给出了相应的低复杂度编码算法。针对现有方向提升计算量过大的缺点:(1)设计了无插值方向模式,提出了可完全重构的快速方向提升LBT,计算量与原有LBT相当。(2)提出了基于裁剪树的全局提升方向优化算法,与现有方向提升块变换(LBT为一种块变换)优化算法相比,计算复杂度由O ( A3 N )降低为O ( AN ),其中A为方向个数,N为像素个数。(3)提出了针对LBT系数特性的量化集合分裂快速编码方法,压缩图像PSNR优于现有方向提升块变换。
本文提出的新型遥感图像变换与编码方法,对于遥感数据的高保真、高速率实时传输具有实用价值。本文中的部分变换及编码技术已经成功应用于航空航天遥感设备的研制中。
With the development of remote sensing, it is becoming more and more difficult to compress remote sensing images with much higher resolution. The traditional transforms used in image compression, such as discrete wavelet transform (DWT), cannot take advantage of geometric regularity in high dimensional signals, which is a central issue to improve compression performance. So, it is critical to develop the transforms with directional selectivity that can represent the anisotropic edges and textures more sparsely. Because remote sensing data must be processed in real time in many cases, the construction of directional transforms with limited redundancy and their fast coding algorithms are the two main challenges.
To get better sparsity, the nature of directions in dual tree (DT) multiscale transform and directional lifting scheme is deeply studied in this thesis. And new fast transforms with improved directional selectivity are constructed. Furthermore, the corresponding efficient codecs are designed and used in remote sensing images compression.
The main contributions in this thesis are as follows.
A new dual-tree structure is proposed, which can represent directional edges and textures in remoting sensing images better. (1) Firstly, the Hilbert transform pair of the high pass filters in DT is defined. Based on the definition, the directional selectivity of DT structure is proved, which is stricter than the explanation based on the analyticity of wavelet functions. (2) Secondly, considering that the filters in the first level DT are not a Hilbert transform pair, a modified DT structure that offers more directional information is proposed. (3) At last, a wavelet pair with better directional selectivity and higher vanishing moments is obtained, by constraining their high pass filters to form a Hilbert transform pair.
A highly efficient codec of DT coefficients is designed based on the proposed DT structure. (1) A direction adaptive context model is developed to reveal the correlation left between adjacent coefficients. (2) The corresponding bands in different trees are proved to be uncorrelated. Using the uncorrelation, a rate-distortion optimization algorithm is proposed and used in DT based compression. Comparing with available DT based compression methods, peak signal-to-noise ratios (PSNR) of our method are 0.1-0.4 dB higher. (3) The influence of denoising on compression in the DT domain is investigated. And a closed-form probability density function (PDF) of noise in DT coefficients is deduced, which approximates the true distribution better comparing with other PDFs now used and gets about 0.3dB coding gain.
A fast directional lifting biorthogonal lapped transform (LBT) is constructed to reduce the computation. (1) The directional mode without interpolation is given and used in directional lifting LBT. It can be performed as efficiently as LBT. (2) An algorithm based on tree pruning is proposed to optimize lifting directions globally. Comparing with the algorithm available, its computation decreases form O ( A3 N ) to O ( AN ), where A is the number of directions and N is the size of the image. (3) A set partition codec is used to code directional lifting LBT coefficients, and the compressed remote sensing images get higher PSNRs.
Our directional transforms and coding algorithms are practical for the high speed and high fidelity transmission of remote sensing images. Some of them have been successfully used in space and aviation remote sensing.
引文
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