CIF: Small: Recovery of Multi-Channel Visual Signals from Limited Color Information Using Rank Minimization and Sparsity Maximization

从捕获的图像和视频信号中恢复视觉颜色是数字成像中最普遍和最基本的问题之一。这个问题影响了数十亿消费者，并影响了这些消费者捕捉、交流和显示的视觉信号的质量。数以百万计的图像和视频摄像头、移动和智能手机以及许多其他类型的可视设备和应用程序都受到了重大影响。例如，几乎所有消费类相机都基于使用滤色器阵列(CFA)的架构，该阵列可捕捉每像素单色图像，以降低成本、尺寸和功耗。因此，需要从捕获的每像素单色CFA图像中恢复原始的三色图像(红-绿-蓝)。尽管在这一领域已经取得了许多贡献和显著的进展，但这个问题在很大程度上仍然没有得到解决。这个项目解决了从有限的颜色信息中恢复多个颜色通道(RMCC)的一般问题。该项目开发了一种用于恢复多个颜色通道的联合秩最小化稀疏最大化(RMSM)框架。矩阵的秩最小化是一种比向量的压缩感知(CS)更一般的框架，它提供了许多强大的工具。该项目以新颖的方式共同瞄准了这两种方法。一个重要的问题是在联合框架下如何在排序最小化和稀疏最大化之间取得最优平衡。此外，这项工作还为稀疏的“颜色”字典范例设计了优化框架。利用过度完整、稀疏的“颜色”词典的概念与以前的工作有很大的不同。该项目还将这项研究的应用扩展到视频去马赛克和视觉编码系统。

The recovery of visual colors from captured images and video signals is among the most prevalent and fundamental problems in digital imaging. This problem affects billions of consumers, and it impacts the quality of the visual signal that these consumers capture, communicate, and display. Millions of image and video cameras, mobile and smart phones, and many other types of visual devices and applications are impacted in a significant way. For example, virtually all consumer cameras are based on an architecture that utilizes a Color Filter Array (CFA), which captures single-color-per-pixel images to reduce cost, size, and power consumption. Hence, one needs to recover the original three color images (Red-Green-Blue) from the captured single-color-per-pixel CFA image. Despite numerous contributions and noticeable progress that has been made in this area, this problem is still largely unsolved.This project addresses the general problem of the recovery of multiple color channels (RMCC) from limited color information. The project develops a joint rank-minimization sparsity-maximization (RMSM) framework for the recovery of multiple color channels. Rank minimization of matrices, which is a more general framework than compressed sensing (CS) of vectors, provides many powerful tools. The project targets both approaches jointly in novel ways. An important question is how to strike an optimal balance between rank-minimization and sparsity-maximization under a joint framework. Furthermore, this effort designs optimization frameworks for a sparsifying "color"-dictionary paradigm. The notion of utilizing overcomplete, sparsifying "color" dictionaries represents a major departure from prior work. The project is also extending the applications of this research to video demosaicing and visual coding systems.