Study On Image Fusion And Denoising With Sparse Representation

Sparse representation (SR) that desires to represent the signal with the least atoms, has been recognized widely. It’s theoretically and practically important to do research on fast sparse representation algorithms in image representation and image processing. This paper takes SR theory as basis, deeply analyzes its application in image processing, focuses on the methods of learning dictionary and constructing the sparse model, and makes an exploratory and innovative study of SR based image processing technology, including image fusion and denoising. The main contents of the paper include:(1) The technology of image features extraction and fusion based on K-SVD (K-singular value decomposition) is studied. In the light of CT-MRI image fusion, an image features extraction and fusion method with K-SVD is presented. By using the K-SVD algorithm, the capabilities of image feature extraction and denoising are strengthen. This method combines the non-zero elements with the "choose-max" rule to fuse the image features separately, so that the definition of image and the capability of preserving the detailed features of the medical image can be improved.Both existing spatial domain and transform domain fusion methods have their own advantages and disadvantages. A combined sparse-spatial representation method based on joint K-SVD is proposed. Firstly, the dictionary corresponding to each image is learned by joint K-SVD. Secondly, the atoms of the dictionary are taken as the image features and combined with the appropriate physical properties to acquire the fused image. The new method can overcome the disadvantages of the definition of image declining and weaker anti-noise-interference ability in spartial domain methods, and lacking the definite physical meanings in transform domain methods.(2) The technology of image fusion based on SR and Piella index optimization is studied. To integrate the processes of image fusion and evaluation, a novel image fusion method with Piella index optimization is proposed. This method can get rid of the blindness in process of image fusion and acquire the optimal fused image in the light of Piella index. To the fusion technology in CS. a novel image fusion algorithm based on Piella index optimization in CS is proposed. This method only needs one complete reconstruction of image to acquire the fused image with a good effect, so it can reduce computation to some extent.The Piella index optimization algorithm is sensitive to noise and has high computation cost. To solve these problems, an image fusion method with SR and Piella index optimization is presented. This method combines the techniques of the SR and Piella index optimization. The atoms of the dictionaries substituting for sparse coefficients are fused with Piella index optimization algorithm. The dimension of the dictionary is usually less than that of the coefficient matrix, so our method can offer a reduction in the computational complexity. Since SR has stronger ability to remove noise, our method is naturally robust to noise. Even if the original images are corrupted with noise, the fused image acquired by our method is still high on Piella index.(3) The technology of image fusion and denoising based on joint sparse representation (JSR) algorithm is studied. Inspired by distributed compressed sensing (DCS), we research the SR algorithm for multiple signals and propose the JSR algorithm. It can calculate the common and unique sparse coefficients of the multiple signals simultaneously. Since the sensors presumably observe related phenomena, the ensemble of signals they acquire can be expected to possess some joint structure, or correlation. The features of each image are generated as combination of two components:the common component, which is present in all images, and the unique component, which is unique to each image. So with the "choose-max" rule, a lot of unique features are discarded, and with the "weighted average" rule, the ratio of weights between each unique feature and the common feature of the fused image drops. To solve these problems, we present an image features extraction and fusion method based on JSR. Since this method can separate the common and unique features of source images and fuse them separately, the fused image can preserve the image features completely and enhance the clarity of the significant features.In order to recover the original images from multiple copies corrupted with the sparse noises, a denoising algorithm with JSR is presented. JSR makes good use of the correlation among the multiple image copies well. All copies share a common component—the image, while each individual measurement contains a unique component—the noise. JSR can separate the common and unique components to denoise the images. The classical denoising algorithm with SR assumes that the noise is non-sparse. It performs suboptimally when the noise is sparse in some dictionary. This method addresses the recovery of original images from multiple copies corrupted with the sparse noises, and it is a useful addition to the classical algorithm.