Introduction to Sparse Representation稀疏表示介绍

作为信号处理中的新兴领域，稀疏表示往往和压缩感知的概念共同出现。压缩感知是为了突破Shannon采样定理中的Nyquist率被提出的一类方法，它旨在通过找到信号中的关键成分从而提升采样效率，并最终降低为了恢复信号所需的最低采样频率。显然，压缩感知适用于信息分布较为集中的信号，也就是稀疏信号。因此，对于信号的稀疏表示正是压缩感知的核心问题之一。
As an emerging field in signal processing, sparse representation often appears together with the concept of compressed sensing. Compressed sensing is a kind of method proposed to break through the Nyquist rate in Shannon sampling theorem. It aims to improve the sampling efficiency by finding the key components in the signal, and finally reduce the minimum sampling frequency needed to restore the signal. Obviously, compressed sensing is applicable to signals with relatively concentrated information distribution, that is, sparse signals. Therefore, the sparse representation of signals is one of the core problems of compressed sensing.

Introduction to This Paper & Its Author, J. Yang本文介绍

杨建超在2011年博士于UIUC的电子与计算机工程系，师从图像超分辨专家Thomas Huang教授，曾在Beckman实验室进行研究，目前在Snapchat任职。他在2008年起开始发表有关图像超分辨的论文（CVPR 2008），目前已发表了6篇相关的顶会、顶刊论文。本文即是杨博士在2010年发表于TIP上的论文，主要内容为介绍一种新颖的基于稀疏表示的单幅图像的超分辨率重建算法，基本思想是通过对高分辨率超完备字典和低分辨率超完备字典进行联合训练以保证它们稀疏表示系数的一致性，这种方法使得局部和全局的相邻图像块之间的兼容性均得到了加强，实验结果表明这种基于图像块先验知识的稀疏表示对普通图像和人脸图像都有很好的效果。
Yang jianchao started his PhD at UIUC's department of electrical and computer engineering in 2011, where he studied under professor Thomas Huang, an expert in superresolution of images, who conducted research in Beckman's lab and is now at Snapchat. He started publishing papers on image superresolution in 2008 (CVPR 2008), and has published six related papers in top conferences and journals. This article published in 2010, Dr Yang is on the TIP of the paper, the main content of this paper introduces a novel based on sparse representation of single image super-resolution reconstruction algorithm, the basic idea is based on high resolution complete dictionary and low resolution ultra complete dictionary on joint training to ensure the consistency of their coefficient of sparse representation, this approach makes the local and global compatibility between adjacent image blocks are strengthened, the experimental results show that the sparse representation based on image block prior knowledge of ordinary image and face image has very good effect.

Introduction引入

1. 本文主要解决稀疏表示中构建字典的问题。根据压缩感知理论，一组好的字典（泛函空间中的正规正交集）有助于将信号转为稀疏信号，因此如何学习到一组合适的字典是稀疏表示和压缩感知的重要问题，其中一种方法是基于数据集进行学习，从而获得适应同类信号的字典。本文的工作在此基础上展开。

2. 本文的观点：通过将低分辨率和高分辨率图像块的联合训练，我们可以强化低分辨率和高分辨率图像块与之对应真实字典稀疏表示的相似性，从而低分辨率图像块的稀疏表示和高分辨率超完备字典一起作用可以重建出高分辨率图像块，然后由高分辨率图像块连接得到最终完整的高分辨率图像。简而言之，就是通过构建低分辨率与高分辨率的字典之间的联系，来实现由低到高的转换。

3. 本文方法的效果：本文方法是一种自适应算法，实现了计算量的降低和算法鲁棒性的提高，在个别任务上优于当前最优模型（2011）。

1. This paper mainly solves the problem of dictionary construction in sparse representation. Based on compressed sensing theory, a set of good dictionary (functional space of normal positive intersection) will help signals into a sparse, so how to learn a set of appropriate dictionary is an important problem of sparse representation and compression perception, one kind of method is based on the data sets to study, to get used to the same signal of the dictionary. The work of this paper is carried out on this basis.

2. This article through the low resolution and high resolution image block joint training, we can strengthen the low resolution and high resolution image block and the corresponding real dictionary of sparse representation of similarity, thus low resolution image block sparse representation and high resolution over complete dictionary work together to rebuild the high resolution image blocks, and then are connected by a high resolution image block final complete high resolution image. In a nutshell, this is a low-resolution to high-resolution transformation by building associations between low-resolution and high-resolution dictionaries.

3. Effect of the method in this paper: the method in this paper is an adaptive algorithm, which can reduce the computation amount and improve the robustness of the algorithm, and is superior to the current optimal model in individual tasks (2011).

1. Problem待解决的问题

2. Existing methods已有方法

3. Our approach本文思路

Algorithm算法

1. Theory理论支撑
2. Coral Code核心代码

Experiment实验

1. Dataset数据
2. Process实验流程
3. Result and Analysis结果展示与分析

Referrence引用

[1] Jianchao Yang, Zhaowen Wang, Zhe Lin, and Thomas Huang. Coupled dictionary training for image super-resolution. To appear in IEEE Transactions on Image Processing (TIP), 2011.
[2] Jianchao Yang, John Wright, Thomas Huang, and Yi Ma. Image super-resolution via sparse representation. IEEE Transactions on Image Processing (TIP), vol. 19, issue 11, 2010.
[3] Jianchao Yang, John Wright, Thomas Huang, and Yi Ma. Image super-resolution as sparse representation of raw image patches. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2008.
[4] Project of ScSR http://www.ifp.illinois.edu/~jyang29/ScSR.htm