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Adaptive and robust sparse learning algorithm for image restoration

English Abstract

Recent years, to imitate the human perceptual system, the sparse representation (SR) technique has been emerging to describe the intrinsic structures of natural images adaptively. Due to its great representation ability, the SR technique has become a powerful tool for handling various image processing tasks, such as, image restoration, segmentation, and recognition. However, for image restoration, current SR models are usually fragile to outliers (e.g., impulse noise or holes). To exploit more robust SR models, in this thesis we study the adaptive sparse representation techniques for image restoration in complicated noisy environment. As an inverse problem, image restoration aims to recover the original degradationfree image from its noisy observation. The degradation comes in many forms such as noise, artifacts, and blurs. Take image denoising as an example. By assuming that the noise follows the Gaussian distribution, several existing SR based learning algorithms combine the self-similarity and sparse representation to exploit intrinsic features of natural images, which have achieved state-of-the-art denoising performance. Nevertheless, these well-known existing learning methods always failed in recovering images corrupted by complicated noise (mixed Gaussian noise and impulse noise). Generally speaking, due to the complicated distribution, the mixed noise are more difficult to be removed. In this thesis, we focus on designing adaptive sparse learning algorithms which are robust to complicated noise. Our main contributions are as follows, • Considering the characteristics of impulse noise (IN), we propose a weighted couple sparse representation model (WCSR) to remove IN in images. In WCSR, a weight vector is incorporated into the loss function to subtly tune the contribution of each pixel to suppress the IN. Moreover, because the reconstructed image contains less noise and share the similar scenario with the original noisefree image, we simultaneously codes the noisy and the reconstructed images to exploit the complicated relationships between them, which helps to improve the reconstruction accuracy. Besides, a dictionary learning algorithm is presented to simultaneously train the dictionary on the raw data directly, which overcomes ii the drawback that the current dictionary learning methods are fragile to outliers. Experimental results demonstrate that the proposed WCSR model can efficiently learn the useful features from the raw data and achieved satisfied IN removal performance. • Self-similarity is a very important prior knowledge in image processing. It assumes that the similar image patches should share similar coefficients, however this ignores the discriminations among the similar signals. Inspired by the fact that the similar signals share similarities but also have differences, a robust bisparsity model (RBSM) is presented to effectively exploit both the similarities and distinctions of signals. We apply the proposed RBSM for mixed noise reduction and experimental results show that our proposed model is superior to several state-of-the-art mixed noise removal methods. • Manifold learning, based on the idea that the similar data points are usually sampled from a low-dimensional manifold, has been successfully embed in sparse learning models. However, the manifold structures of data will be severely destroyed by outliers. To address this concern, we propose a weighted joint sparse representation (WJSR) model to simultaneously encode a set of data samples that are drawn from the same subspace but corrupted with noise and outliers. Our model is desirable to explore the common information shared by these data samples while reducing the influence of outliers. We further introduce a greedy algorithm called weighted simultaneous OMP (W-SOMP) to efficiently approximate the global optimal solution of the proposed model.

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Liu, Li Cheng


Faculty of Science and Technology


Department of Computer and Information Science




Image reconstruction -- Mathematical models

Image processing -- Digital techniques


Chen, C. L.

Chen, Long

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