Graph Transform Optimization With Application to Image Compression
Graph Transform Optimization With Application to Image Compression
复制标题
图变换优化及其在图像压缩中的应用
DOI：
10.1109/tip.2019.2932853
复制
发表时间：
2017
影响因子：
10.6
通讯作者：
P. Frossard
中科院分区：
文献类型：
--
作者：
Giulia Fracastoro;D. Thanou;P. Frossard
在本文中，我们提出了一种新的基于图的变换，并说明了其在信号压缩中的潜在应用。我们的方法依赖于图的精心设计，通过有效的基于图的变换来优化整体率失真性能。我们引入了一种新颖的图估计算法，该算法通过考虑速率失真项中的信号和图拓扑的编码来揭示图信号值之间的连接性。特别是，我们通过将边权重视为位于对偶图上的另一个图信号，为图引入了一种新颖的编码解决方案。然后，通过最小化对偶图上的图傅里叶变换（GFT）系数的稀疏性，在优化问题中引入图描述的成本。这样，我们就得到了一个凸优化问题，其解定义了一个有效的变换编码策略。所提出的技术是一个可以应用于不同类型信号的通用框架，我们展示了两个可能的应用领域，即自然图像编码和分段平滑图像编码。实验结果表明，所提出的基于图的变换优于经典的固定变换，例如自然图像和分段平滑图像的 DCT。在深度图编码的情况下，所获得的结果甚至可以与专门为深度图图像设计的最先进的基于图的编码方法相媲美。
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an effective graph-based transform. We introduce a novel graph estimation algorithm, which uncovers the connectivities between the graph signal values by taking into consideration the coding of both the signal and the graph topology in rate-distortion terms. In particular, we introduce a novel coding solution for the graph by treating the edge weights as another graph signal that lies on the dual graph. Then, the cost of the graph description is introduced in the optimization problem by minimizing the sparsity of the coefficients of its graph Fourier transform (GFT) on the dual graph. In this way, we obtain a convex optimization problem whose solution defines an efficient transform coding strategy. The proposed technique is a general framework that can be applied to different types of signals, and we show two possible application fields, namely natural image coding and piecewise smooth image coding. Experimental results show that the proposed graph-based transform outperforms classical fixed transforms, such as DCT for both natural and piecewise smooth images. In the case of depth map coding, the obtained results are even comparable to the state-of-the-art graph-based coding method that is specifically designed for depth map images.