Improvement of DCT-Based Compression Algorithms Using Poisson's Equation
Improvement of DCT-Based Compression Algorithms Using Poisson's Equation
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DOI：
10.1109/tip.2006.882005
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发表时间：
2006-12
影响因子：
10.6
通讯作者：
K. Yamatani;N. Saito
中科院分区：
文献类型：
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作者：
K. Yamatani;N. Saito
我们提出了两种新的图像压缩-解压缩方法，它们以更好的视觉保真度、更少的阻塞伪影和更好的PSNR再现图像，特别是在低比特率下，与相同比特率下的JPEG基线方法处理的图像相比。额外的计算成本很小，即与输入图像中的像素数成线性比例。第一种方法，“全模式”多谐局部余弦变换（PHLCT），修改JPEG基线方法的编码器和解码器部分。全模式PHLCT的目标是减少编码部分的代码大小，减少解码器部分的阻塞工件。第二种是“部分模式”PHLCT（简称PPHLCT），它只修改解码器部分，因此，它接受JPEG文件，并以更高的质量和更少的阻塞工件解压缩它们。这些算法背后的关键思想是将每个图像块分解为多谐波分量和残差。本文的多谐分量是泊松方程的近似解，具有Neumann边界条件，这意味着它是原始图像块的平滑预测器，仅使用图像块边界上的图像梯度信息。因此，通过从原始图像块中去除多谐波分量获得的残差在块边界上具有近似为零的梯度，这导致了快速衰减的DCT系数，这反过来又导致了相同比特率下更有效的压缩-解压缩算法。我们证明了每个块的多谐分量可以仅通过该块及其相邻块的DCT系数矩阵的第一列和行来估计，并且可以比以前提出的一些其他AC预测方法更好地预测原始图像数据。我们的数值实验客观和主观地证明了PHLCT方法相对于JPEG基线方法的优越性，以及PPHLCT方法对JPEG压缩图像的解压效果
We propose two new image compression-decompression methods that reproduce images with better visual fidelity, less blocking artifacts, and better PSNR, particularly in low bit rates, than those processed by the JPEG Baseline method at the same bit rates. The additional computational cost is small, i.e., linearly proportional to the number of pixels in an input image. The first method, the "full mode" polyharmonic local cosine transform (PHLCT), modifies the encoder and decoder parts of the JPEG Baseline method. The goal of the full mode PHLCT is to reduce the code size in the encoding part and reduce the blocking artifacts in the decoder part. The second one, the "partial mode" PHLCT (or PPHLCT for short), modifies only the decoder part, and consequently, accepts the JPEG files, yet decompresses them with higher quality with less blocking artifacts. The key idea behind these algorithms is a decomposition of each image block into a polyharmonic component and a residual. The polyharmonic component in this paper is an approximate solution to Poisson's equation with the Neumann boundary condition, which means that it is a smooth predictor of the original image block only using the image gradient information across the block boundary. Thus, the residual-obtained by removing the polyharmonic component from the original image block-has approximately zero gradient across the block boundary, which gives rise to the fast-decaying DCT coefficients, which, in turn, lead to more efficient compression-decompression algorithms for the same bit rates. We show that the polyharmonic component of each block can be estimated solely by the first column and row of the DCT coefficient matrix of that block and those of its adjacent blocks and can predict an original image data better than some of the other AC prediction methods previously proposed. Our numerical experiments objectively and subjectively demonstrate the superiority of PHLCT over the JPEG Baseline method and the improvement of the JPEG-compressed images when decompressed by PPHLCT