基于稀疏冗余表示和字典学习的图像去噪方法研究外文翻译资料

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标题：

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

基于稀疏冗余表示和字典学习的图像去噪方法研究

摘要：

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.

我们应对要去除其中零均值齐加性高斯白噪声的图像去噪问题，所采取的方法是基于稀疏和冗余表示的训练字典。使用K-SVD算法，我们可以获得一个有效描述图像内容的字典。同时两种字典训练选项可以选择：使用本身嘈杂的图像，或在高质量图像的数据库的基础上进行训练。由于K-SVD在处理小图像块方面受到限制，我们通过定义全局图像将其部署扩展到任意图像大小，然后在图像中的每个位置上强制执行稀疏。我们展示了贝叶斯方法如何引导一个简单有效的去噪算法，这展现了最先进的去噪性能，其效果近似于甚至超过了最近发布的可选去噪方法。

Index Terms—Bayesian reconstruction, dictionary learning, discrete cosine transform (DCT), image denoising, K-SVD, matching pursuit, maximum a posteriori (MAP) estimation, redundancy, sparse representations.

索引术语 - 贝叶斯重建，字典学习，离散余弦变换（DCT），图像去噪，K-SVD，匹配追踪，最大后验概率（MAP）估计，冗余，稀疏表示。

正文：

I. INTRODUCTION 第一章 介绍

In this paper, we address the classic image denoising problem: An ideal image X is measured in the presence of an additive zero-mean white and homogeneous Gaussian noise, V, with standard deviation. The measured image Y is, thus

We desire to design an algorithm that can remove the noise from Y, getting as close as possible to the original image, X .

在本文中，我们解决了经典的图像去噪问题：一个理想的图像X是在存在标准偏差的零均值齐加性高斯白噪声V下测量的。 因此，测量的图像Y是

我们希望设计一种可以消除测量图像Y的噪声的算法，使其尽可能靠近原始图像X。

The image denoising problem is important, not only because of the evident applications it serves. Being the simplest possible inverse problem, it provides a convenient platform over which image processing ideas and techniques can be assessed. Indeed, numerous contributions in the past 50 years or so addressed this problem from many and diverse points of view. Statistical estimators of all sorts, spatial adaptive filters, stochastic analysis, partial differential equations, transform-domain methods, splines and other approximation theory methods, morphological analysis, order statistics, and more, are some of the many directions explored in studying this problem. In this paper, we have no intention to provide a survey of this vast activity. Instead,we intend to concentrate on one specific approach towards the image denoising problem that we find to be highly effective and promising: the use ofsparse and redundant representations over trained dictionaries.

图像去噪问题很重要，不仅因为其应用的明显优势。作为最简单的逆推，它提供了一个方便的平台，可以对图像处理的方法和技术进行评估。事实上，过去五十年来，无数的文献从许多不同的角度试图解决这个问题。各种统计估计，空间自适应滤波，随机分析，偏微分方程，变换域方法，样条等近似理论方法，形态分析，顺序统计等等，都是研究这一问题的方向。在本文中，我们无意对其提供广泛的调查。相反，我们打算专注于一种针对图像去噪问题的具体方法，我们发现这是非常有效和有希望的：即对训练词典使用稀疏冗余的表示。

Using redundant representations and sparsity as driving forces for denoising of signals has drawn a lot of research attention in the past decade or so. At first, sparsity of the unitary wavelet coefficients was considered, leading to the celebrated shrinkage algorithm [1]–[9]. One reason to turn to redundant representations was the desire to have the shift invariance property [10]. Also, with the growing realization that regular separable 1-D wavelets are inappropriate for handling images, several new tailored multiscale and directional redundant transforms were introduced, including the curvelet [11], [12], contourlet [13], [14], wedgelet [15], bandlet [16], [17], and the steerable wavelet [18], [19]. In parallel, the introduction of the matching pursuit [20], [21] and the basis pursuit denoising [22] gave rise to the ability to address the image denoising problem as a direct sparse decomposition technique over redundant dictionaries. All these lead to what is considered today as some of the best available image denoising methods (see [23]–[26] for few representative works).

使用冗余和稀疏表示作为信号去噪的推动力在过去十多年来引起了大量的研究关注。首先，由于单一小波系数的稀疏性，产生了著名的收缩算法[1] - [9]。而转向冗余表示的一个原因是希望拥有移位不变性[10]。此外，随着越来越多的研究我们认识到，常规可分离的1-D小波不适合处理图像，于是数个新的定向多尺度和定向冗余变换被引入，包括曲波[11][12]，轮廓波[13][14]，楔形波[15]，束带波[16][17]和可操纵小波[18][19]。同时，匹配追求[20][21]和基本追求去噪[22]的引入提供了解决图像去噪问题的能力，即冗余词典的直接稀疏分解技术。如今这些方法都被认为是最好的图像去噪方法之一（参见[23] - [26]几个代表成果）。

While the work reported here is also built on the very same sparsity and redundancy concepts, it is adopting a different point of view, drawing from yet another recent line of work that studies example-based restoration. In addressing general inverse problems in image processing using the Bayesian approach, an image prior is necessary. Traditionally, this has been handled by choosing a prior based on some simplifying assumptions, such as spatial smoothness, low/max-entropy, or sparsity in some transform domain. While these common approaches lean on a guess of a mathematical expression for the image prior, the example-based techniques suggest to learn the prior from images somehow. For example, assuming a spatial smoothness-based Markov random field prior of a specific structure, one can still question (and, thus, train) the derivative filters to apply on the image, and the robust function to use in weighting these filtersrsquo; outcome [27]–[29].

虽然这里报告的研究成果也建立在相同的稀疏性和冗余性概念上，但它采用不同的观点，参考了另一个最新的研究成果来研究基于实例的恢复绘图。在使用贝叶斯方法解决图像处理的一般逆问题，需要先前的图像。传统上，这已经通过选择现有基于某些简化假设来处理，如空间平滑度，低/最大熵，或在一些变换域的稀疏度。虽然这些常见的方法依赖于图像的数学表达式的猜测，但基于示例的技术建议以某种方式学习之前的图像。例如，假设在特定结构之前的基于空间平滑度的马尔科夫随机场，人们仍然可以质疑（并训练）导数滤波器以应用于图像，以及用于加权这些

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