Research On Sparse Representation Based Image Denoising And Super-resolution Reconstruction Algorithm

With the rapidly developing of the computer and digital technology, the digitalimage has become one of the important methods of information storage andtransformation in society. The space resolution and SNR of digital image have occupiedgreat importance as for image quality assessment. In practical application, users alwayslook forward to a clean, high quality of image. However, in the actual process ofimaging, due to the limitations of the degraded factors such as down-sampling, motionblurring, atmospheric turbulence, noising, etc. It is not always easy to capture a desiredhigh-resolution image, which causes many difficulties in image processing and analysis,leading to an obstacle in correctly understanding the laws of the objective world.Therefore, it is challenging and urgent demand to improve the quality of an image.In recent years, sparse representation theory has attracted much attention ofscholars and it has been successfully applied in the field of image denoising and imagesuper-resolution. By means of designing and choosing a proper over-completedictionary, sparse representation can effectively obtain essential features of an image, aswell as represent the image concisely. Based on learning-based sparse representationtheory, the focal points of this paper include relevant key issues in image denoising andsingle image super-resolution. Main contents and contributions include:(1) The paper expounds the image sparse representation theory, includingmathematical model, the sparse degree measurement, signal incoherence and optimizedalgorithm. And the paper also describes the related algorithm of sparse and low-rankmatrix decomposition and dictionary learning, which is based on sparse representationtheory.(2) The paper introduces and studies the image denoising methods. Bydecomposing, the image gets the low rank part and the sparse part. Meanwhile, as thepre-denoising image, low rank part contains the most of the image information. On theother hand, the image sparse part which has been denoised by the median filter includespart of the high frequency texture details of the image. The two parts merged into thefinal denoising image. The experimental result indicates that the algorithm can reservefringe detail of image while removing the noise, and provides new thinking for image denoising. The PSNR improves about3~5dB than the general denoising method.(3) The P_BM3D denoising method is presented by pretreatment denoisingmethodology for distinguish between different areas of the image. The P_BM3Dmethod can effectively remove the salt noise in dark-colored area and the pepper noisein light-colored area while does not lose the useful information for original image, it’sabout making the BM3D algorithm can effectively interact and also show good andstable denoising performance for filtering out both Gaussian and salt and pepper noisein image.The PSNR improves about4~7dB than the general denoising method.(4) We combine the idea of dictionary learning and the idea of image denoising inthis work, expounding the image denoising problem based on sparse and redundantrepresentations over trained dictionaries and giving experiment and theory analysis inthe end.When denoised a given image from mixed noise with pepper and salt noise, theImage Denoising algorithm via sparse and redundant representations over learneddictionaries will retain pepper and salt noise in the image as the details. Through in deepexperimentation and theoretic analysis, we apply a post-processing algorithm which canwipe the pepper and salt noise off after denoising image via over learned dictionary,increased flexibility and adaptability of the denoising algorithm via sparse andredundant representations over learned dictionaries.(5) A valid sample set construction method is proposed. By setting a reasonablethreshold value of Euclidean distance similarity, the proposed method can ensure thatthe constructed sample set have structural anisotropy and diversity. Comparing with theformer method, the method proposed significantly decreases the dictionary training timeand improves the quality of the reconstructed image, and decreases for50%indictionary practice.(6) Based on the algorithm of sparse and low-rank matrix decomposition toestablish a couple set of training sample, we propose the image super-resolutionreconstruction algorithm with adopting improving dictionary learning method. Thiswork rebuild the high and low resolution training sample by decomposing the wholeimage use IALM algorithm, and drives multiple dictionary updates K-SVD method forupdating the dictionary, meanwhile combine the OMP algorithm and coefficient reuseCoefROMP algorithm for solving the sparse coefficients and reestablish the highresolution image. Moreover, the proposed method performs better for detail and texture recover, and also can reduce the artifacts around edge in the reconstructed HR image,improving the dictionary training efficiency and getting better visual effect.Above all, on the basis of the fundamental theory of the image sparserepresentation, this thesis has already researched in the work of image denoising theoryand image super-resolution reconstruction technology in two ways and proposed someinnovations. The proposed methods can effectively overcome the limitations of theexisting methods and achieve better applicability in low-quality images recovery, alsoexpand new ideas for relevance direction about digital image processing technique.