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The Power of Complementary Regularizers: Image Recovery via Transform Learning and Low-Rank Modeling

2018-08-03 19:29:19
Bihan Wen, Yanjun Li, Yoram Bresler

Abstract

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.

Abstract (translated)

最近关于自适应稀疏和低秩信号建模的工作已经证明了它们在各种图像/视频处理应用中的有用性。基于补丁的方法利用本地补丁稀疏性,而其他工作应用低级别的分组补丁来利用图像非局部结构。但是,单独使用任一方法通常会限制图像重建或恢复应用程序的性能。在这项工作中,我们提出了一个同时稀疏和低秩模型,称为STROLLR,以更好地代表自然图像。为了充分利用局部和非局部图像属性,我们使用具有联合低秩正则化的变换学习方案开发了图像恢复框架。该方法的一些计算效率和良好性能归功于自适应稀疏表示的变换学习的使用,而不是流行的合成字典学习算法,其涉及NP-硬稀疏编码的近似和昂贵的学习步骤。我们在各种应用中演示了所提出的框架,用于图像去噪,修复和压缩感知的磁共振成像。与最先进的竞争方法相比,结果显示出有希望的性能。

URL

https://arxiv.org/abs/1808.01316

PDF

https://arxiv.org/pdf/1808.01316.pdf


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