Applications Of The Models And Algorithms Based On Non-convex Optimization To Processing Medical And Remote Sensing Images

Technologies of digital image processing have practical significance and wide applications.Due to limitation of imaging hardware,acquisition and transmission of images acquired,and the influence of the internal electronic components and external environments,acquired images often have some drawbacks such as data loss in the images,low spatial resolution,too large image data for transmission and storage,and so on.These subjects are frontier research topics.Based on medical images,multi-spectral and hyperspectral remote sensing images non-convex optimization models and the corresponding computation algorithms were developed and implemented,respectively,for image segmentation,image inpainting,image super-resolution reconstruction,and multispectral and hyperspectral image compressive sensing.This dissertation is consisted of the following four main components:1.Image segmentation: In this component,we use the cosine function to express the data energy fitting of the traditional active contours model and propose a model based on sectional image recovery local cosine fitting energy active contours,which is used to segment medical and synthetic images.It can process synthetic images with intensity inhomogeneity.In addition,we formatted the model in a discrete form,which is more convenient to add a regular term to control the segmentation.So the computational complexity is reduced,caused by re-initializing the level set curve.The improved algorithm is utilized to segment medical images and three-dimensional visualization results are obtained.Experimental results indicate that the segmentation results are accurate and efficient when applied to different kinds of images.2.Recovery of missing stripes in satellite images: On May 31,2003,the scan line corrector(SLC)of the Enhanced Thematic Mapper Plus(ETM+)on board the Landsat-7 satellite fail,resulting in strips of data lost in all ETM+ images acquired since then.In this study,we propose a novel inpainting algorithm for recovering the ETM+ SLC-OFF images.The two slopes of the boundaries of each missing stripe are extracted through the Hough transform,ignoring the slope of the edge of the strip that overlaps the edge of the image.An adaptive dictionary is then developed and trained using ETM+ SLC-ON images acquired before May 31,2003 so that the physical characteristics and geometric features of the ground coverage of the data-missing strips can be considered during recovery.To make the algorithm computationally efficient,data-missing strips are repaired along their slope directions by using the()logdet low-rank non-convex model along with the dictionary.Results show that the ETM+ images restore using the new algorithm have lower RMSE,higher PSNR and SSIM values,and better visualization.3.Super-resolution of remote sensing images: In the field of remote sensing image processing for earth and environmental applications,super-resolution(SR)is a useful image enhancement technique that reconstructs high-resolution(HR)images from lowresolution(LR)images.A novel SR algorithm is developed that consists of the following steps:(1)A LR image is Fourier transformed to frequency domain.(2)The image in the frequency domain is then expanded to the same size(same number of pixels)as a HR image that is desired.(3)The expanded image in frequency domain is then inverse Fourier transformed to the space domain to form a primary HR image.(4)A final HR image is reconstructed from the primary HR image.This algorithm is based on a low-rank regularization model in which a non-local smoothed rank function(SRF)is used.This new SR algorithm is thus called the Frequency Domain Expansion with Reconstruction from Compressed Representation(FDE-RCR)algorithm.Results show that the newly developed SR algorithm overcomes the deficiency of the SR algorithms that are based on frequency domain in reconstructing HR images from noisy LR images and obtains better reconstruction results in terms of lower root-mean-square error(RMSE),peak signal-tonoise ratio(PSNR),and structure similarity(SSIM).4.Compressive sensing(CS): CS of a low-rank tensor has attracted much attention in the application of multispectral and hyperspectral remote sensing.In this study we proposed to use the sparseness and low-rankness of a tensor between tensor cubes,to get better reconstruction results in reconstructing a 3D tensor than other algorithms.Firstly,the tensor CS reconstruction algorithm is developed by using the non-local low-rank regularization and variational framework.Secondly,the cube grouping and the nonconvex Laplacian function are used,and the regularization/penalty method was used to constrain the tensor CS reconstruction model.Finally,to effectually solve the minimization problem of the rank,the alternating direction method of multipliers(ADMM)method is used.The method of low-rank approximation regularization of the non-convex non-local Laplacian function can obtain more accurate reconstruction results than some common alternative low-rank methods.Results from numerical experiments show that the proposed tensor CS reconstruction based on the non-local TCS-NL-Laplacian regularization algorithm preserves well the wide range of information in remote sensing images with various noise levels and is effective and stable in reconstructing 3D tensor images.