基于稀疏表示的图像超分辨率重建研究

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"sr paper图像超分辨 - 图像超分辨的经典文章杨建超 - super resolution" 本文《Image Super-Resolution as Sparse Representation of Raw Image Patches》由杨建超等人撰写，探讨了如何从单个低分辨率输入图像生成高分辨率图像的问题。文章基于压缩感知（compressed sensing）理论来解决这一挑战，将低分辨率图像视为高分辨率图像的下采样版本，假设高分辨率图像的区域（patches）在过度完备的原型信号原子字典中具有稀疏表示。压缩感知的核心思想是，在温和的条件下，即使是从下采样的信号中，也能准确恢复出稀疏表示。对于图像超分辨率问题而言，稀疏性作为先验知识，可以用来正则化原本无解的逆问题，使得重建过程更加稳定且效果更优。作者进一步指出，从与输入图像具有相似统计特性的训练图像中随机选取的一小部分原始图像块（raw patches），通常可以作为良好的基础来构建这个过度完备字典。这是因为这些随机选取的patch能捕获图像的基本结构和模式，有助于高分辨率图像的重建。文章通过实验展示了在稀疏表示框架下进行图像超分辨率的有效性，这种方法不仅能够提升图像的细节清晰度，还能保持图像的整体结构和自然感。同时，由于依赖于训练图像的统计特性，这种方法对于不同类型的图像可能具有一定的泛化能力。此外，该研究对图像处理领域具有重要意义，因为它提供了一种新的思路来处理传统上被认为非常困难的超分辨率问题。通过利用稀疏表示和压缩感知，可以在计算复杂度相对较低的情况下，实现高分辨率图像的高质量重建，这对于视频监控、医学成像、遥感图像分析等多个领域都有潜在的应用价值。这篇论文是图像超分辨率领域的经典之作，它引入了压缩感知和稀疏表示的概念，为后续的深入研究和技术创新奠定了基础。

Image Super-Resolution as Sparse Representation of Raw Image Patches

Jianchao Yang

†

, John Wright

‡

, Thomas Huang

†

,YiMa

‡

ECE Department, University of Illinois at Urbana-Champagin, USA

Beckman Institute

†

and Coordinated Science Laboratory

‡

{jyang29, jnwright, huang, yima@uiuc.edu}

Abstract

This paper addresses the problem of generating a super-

resolution (SR) image from a single low-resolution input

image. We approach this problem from the perspective of

compressed sensing. The low-resolution image is viewed

as downsampled version of a high-resolution image, whose

patches are assumed to have a sparse representation with

respect to an over-complete dictionary of prototype signal-

atoms. The principle of compressed sensing ensures that

under mild conditions, the sparse representation can be

correctly recovered from the downsampled signal. We will

demonstrate the effectiveness of sparsity as a prior for reg-

ularizing the otherwise ill-posed super-resolution problem.

We further show that a small set of randomly chosen raw

patches from training images of similar statistical nature to

the input image generally serve as a good dictionary, in the

sense that the computed representation is sparse and the

recovered high-resolution image is competitive or even su-

perior in quality to images produced by other SR methods.

1. Introduction

Conventional approaches to generating a super-

resolution (SR) image require multiple low-resolution

images of the same scene, typically aligned with sub-pixel

accuracy. The SR task is cast as the inverse problem of

recovering the original high-resolution image by fusing

the low-resolution images, based on assumptions or

prior knowledge about the generation model from the

high-resolution image to the low-resolution images. The

basic reconstruction constraint is that applying the image

formation model to the recovered image should produce

the same low-resolution images. However, because much

information is lost in the high-to-low generation process,

the reconstruction problem is severely underdetermined,

and the solution is not unique. Various methods have been

proposed to further regularize the problem. For instance,

one can choose a MAP (maximum a-posteriori) solution

under generic image priors such as Huber MRF (Markov

Random Field) and Bilateral Total Variation [14, 11, 25].

However, the performance of these reconstruction-based

super-resolution algorithms degrades rapidly if the mag-

niﬁcation factor is large or if there are not enough low-

resolution images to constrain the solution, as in the ex-

treme case of only a single low-resolution input image [2].

Another class of super-resolution methods that can over-

come this difﬁculty are learning based approaches, which

use a learned co-occurrence prior to predict the correspon-

dence between low-resolution and high-resolution image

patches [12, 26, 16, 5, 20].

In [12], the authors propose an example-based learn-

ing strategy that applies to generic images where the low-

resolution to high-resolution prediction is learned via a

Markov Random Field (MRF) solved by belief propaga-

tion. [23] extends this approach by using the Primal Sketch

priors to enhance blurred edges, ridges and corners. Nev-

ertheless, the above methods typically require enormous

databases of millions of high-resolution and low-resolution

patch pairs to make the databases expressive enough. In [ 5],

the authors adopt the philosophy of LLE [22] from manifold

learning, assuming similarity between the two manifolds in

the high-resolution patch space and the low-resolution patch

space. Their algorithm maps the local geometry of the low-

resolution patch space to the high-resolution patch space,

generating high-resolution patch as a linear combination of

neighbors. Using this strategy, more patch patterns can be

represented using a smaller training database. However, us-

ing a ﬁxed number K neighbors for reconstruction often re-

sults in blurring effects, due to over- or under-ﬁtting.

In this paper, we focus on the problem of recovering

the super-resolution version of a given low-resolution im-

age. Although our method can be readily extended to han-

dle multiple input images, we mostly deal with a single in-

put image. Like the aforementioned learning-based meth-

ods, we will rely on patches from example images. Our

method does not require any learning on the high-resolution

patches, instead working directly with the low-resolution

training patches or their features. Our approach is motivated

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