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Random Walk Graph Laplacian based Smoothness Prior for Soft Decoding of JPEG Images

机译：基于随机游走图拉普拉斯算子的软译码先验   JpEG图像

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摘要

Given the prevalence of JPEG compressed images, optimizing imagereconstruction from the compressed format remains an important problem. Insteadof simply reconstructing a pixel block from the centers of indexed DCTcoefficient quantization bins (hard decoding), soft decoding reconstructs ablock by selecting appropriate coefficient values within the indexed bins withthe help of signal priors. The challenge thus lies in how to define suitablepriors and apply them effectively. In this paper, we combine three image priors---Laplacian prior for DCTcoefficients, sparsity prior and graph-signal smoothness prior for imagepatches---to construct an efficient JPEG soft decoding algorithm. Specifically,we first use the Laplacian prior to compute a minimum mean square error (MMSE)initial solution for each code block. Next, we show that while the sparsityprior can reduce block artifacts, limiting the size of the over-completedictionary (to lower computation) would lead to poor recovery of high DCTfrequencies. To alleviate this problem, we design a new graph-signal smoothnessprior (desired signal has mainly low graph frequencies) based on the lefteigenvectors of the random walk graph Laplacian matrix (LERaG). Compared toprevious graph-signal smoothness priors, LERaG has desirable image filteringproperties with low computation overhead. We demonstrate how LERaG canfacilitate recovery of high DCT frequencies of a piecewise smooth (PWS) signalvia an interpretation of low graph frequency components as relaxed solutions tonormalized cut in spectral clustering. Finally, we construct a soft decodingalgorithm using the three signal priors with appropriate prior weights.Experimental results show that our proposal outperforms state-of-the-art softdecoding algorithms in both objective and subjective evaluations noticeably.
机译：考虑到JPEG压缩图像的盛行，从压缩格式优化图像重建仍然是一个重要问题。代替从索引的DCT系数量化仓的中心简单地重建像素块（硬解码），软解码通过在先验信号的帮助下通过在索引的仓中选择适当的系数值来重建块。因此，挑战在于如何定义合适的先验并有效地应用它们。在本文中，我们结合了三种图像先验-DCT系数的拉普拉斯先验，图像补丁的稀疏性先验和图信号平滑先验-来构造有效的JPEG软解码算法。具体来说，我们首先使用Laplacian来为每个代码块计算最小均方误差（MMSE）初始解。接下来，我们表明尽管稀疏优先级可以减少块伪像，但限制过度完成的字典的大小（以降低计算量）将导致高DCT频率的恢复不佳。为了缓解这个问题，我们基于随机游动图拉普拉斯矩阵（LERaG）的左本征向量设计了一种新的图形信号平滑度优先级（所需信号主要具有较低的图形频率）。与先前的图形信号平滑度先验相比，LERaG具有令人满意的图像过滤特性，并且具有较低的计算开销。我们演示了LERaG如何通过将低图频率分量解释为频谱聚类中归一化割的松弛解来促进分段平滑（PWS）信号的高DCT频率的恢复。最后，我们使用三个具有适当优先权的先验信号构造了软解码算法。实验结果表明，我们的建议在客观和主观评估方面均优于最新的软解码算法。

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