Research On Image Denoising Method Based On Compressive Sensing

As a new field derived from Applied Mathematics and computer science, the technologyof digital image processing is widely in people’s daily life. Image denoising is one of thewidely studied topics in this field. Its objective is to recover the best estimate of the originalimage from its nosy version. Now there are more and more in-depth studies on imagedenoising, and it will be the development of this field with breaking the traditional pattern andbringing in new technology.Compressive sensing is an emerging science in recent years, it blazed a new path forsignal processing field, the core idea of which is using few measurement data with muchsmaller than the Nyquist sampling rate to realize signal reconstruction, and can save the costof signal processing. This paper mainly research on the applications of compressive sensing inimage denoising field, constructing the mathematical model of image denosing based oncompressive sensing. The main work of this paper as follows:The framework of compressive sensing is introduced, including sparse representation,the construction of measurement matrix and the reconstruction algorithm.Several classical reconstruction algorithms are introduced, and achieve a new improvedOMP method by adding a weighted matrix, which can improve the sparsity of the image toget a sparse representation more accurately. The experiments show that this method isfeasible.Several traditional image denoising algorithms are introduced, and an new imagedenoising method via Clustering-Based Sparse Representation over collaborative filter isproposed, It employes collaborative filters to extract high-frequency components on the noisyimage, and then using the K-means method for clustering. It using the compressive sensingtheory to represent the high-frequency components, and then using the reconstructionalgorithm to build the denoised image by adding the low-frequency components. Theexperiments shows that this method can protect the information of image structure effectivelyand promote the result of denoising greatly.Owing to the limitations on the noise variance of Several image denoising algorithmssuch as K-SVD、BM3D, a new compressive sensing image denoising algorithm based onspectral clustering is proposed. Firstly, it uses a simple hard thresholding scheme to obtain theinitial estimate,and then dividing the whole image up into similarity nets based on spectralclustering, and then constructs a denoising model by using the compressive sensing. Theexperiments show that this method is feasible and effective even though no assumption onnoise variance is made.