Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final value of those samples that are estimated more than once needs to be decided in some way. Averaging, the simplest approach, often leads to unsatisfactory results. Significant work has been devoted to this issue in recent years. Several works explore the idea of a weighted average of the overlapped patches and/or pixels; others promote agreement (consensus) between the patches at their intersections. Agreement can be either encouraged or imposed as a hard constraint. This work develops on the latter case. The result is a variational signal processing framework, named PACO, which features a number of appealing theoretical and practical properties. The PACO framework consists of a variational formulation that fits a wide variety of problems, and a general ADMMbased algorithm for minimizing the resulting energies. As a byproduct, we show that the consensus step of the algorithm, which is the main bottleneck of similar methods, can be solved efficiently and easily for any arbitrary patch decomposition scheme. We demonstrate the flexibility and power of PACO on three different problems: image inpainting (which we have already covered in previous works), image denoising, and contrast enhancement, using different cost functions including Laplacian and Gaussian Mixture Models.
翻译:许多信号处理算法将目标信号破碎成重叠部分(也称为窗口或补丁),分别处理它们,然后将其缝合,以产生统一的输出。在重叠时,需要以某种方式决定那些估计超过一次的样本的最终价值。 通化是最简单的方法,往往导致不满意的结果。 近些年来,对这个问题做了大量的工作。 一些工作探索了将重叠的补丁和/或像素加权平均值的构想; 另一些工作则促进在交叉点的补丁之间达成一致(共识) 。 协议可以作为一种硬性制约加以鼓励或强制实施。 这项工作在后一种情况下发展。 结果是一个变异信号处理框架, 名为 PACO, 含有许多吸引理论和实践属性。 PACO 框架包含一种适应各种问题的变异配方配方, 以及一个基于ADMMM的通用算法, 以尽量减少由此产生的能量。 作为副产品, 我们展示了算法的共识步骤, 也就是类似方法的主要瓶颈, 能够高效和容易地解决任何任意的变异性信号处理过程, 。 我们展示了先前的变式变式变式变式变式变式图和变式图, 。