Image Super-resolution Reconstruction Algorithm Based On Compressive Sensing

As we all know, digital images have in depth people’s lives such as remote sensingimage security monitoring and medical imaging. The quality of images has become highand growing, trying to supply people’s need. How to acquire high-resolution images hasbecome a hot area of research for several years. Super-resolution image reconstructionproduces a high-resolution image from a set of low-resolution images. Due to limitationsof imaging devices and techniques, we can always acquire low-resolution images.However，we can obtain more detailed information from a set of low-resolution images.And then we can reconstruct a high-resolution image by image super-resolution technologymaking use of the fused image that contains all these detailed information.Compressive sensing has developed in recent years. This takes advantage of thesignal’s sparseness or compressibility in some domain, allowing the entire signal to bedetermined from relatively few measurements. Development and application ofcompressive sensing have become very popular in research of digital image processing.The reconstruction algorithm is the key point that most researchers focus on and significantprogress has been made.First, we study main content of image super-resolution reconstruction. Next, weintroduce the image registration, image fusion and image reconstruction in detail. And thenwe introduce the valuation criteria of the image quality.Second, we have classified the image registration according to different application.And we study the SIFT and make a mass of simulation to testify that the algorithm hasinvariant character for translation, rotation and scale. In addition, Laplacian Pyramidalfusion algorithm has been studied and testified by MATLAB.Third, we make a summing up of image super resolution algorithms. And we analyzenon-uniform interpolation, iterated back projection, maximum a posterior and projectiononto convex sets in detail. Four algorithms have been simulated. Interpolation algorithmbased on region division has been introduced into POCS, and then a2-D nonlinear filter isused for iteration. The study proved that the results of the proposed approach are better inimage detail.Finally, it is documented that we can use compressive sensing theory to make anaccurate estimate of the original high-resolution image since the image is highly compressible in the wavelet domain. We incorporate a down sampling low-pass filter intoour measurement matrix to allow the super resolution problem meet the restricted isometryproperty of compressive sensing theory. We study orthogonal matching pursuit in detail.However, one of the main shortcomings of OMP is its irreversible selection is morecomplicated due to a sequence of least squares (LS) problems solved in greedy iterations.And it is inefficiency by only taking one atom for every iteration. We modified OMP byusing dichotomous coordinate descent iterations and identifying K dimensional support-setin every iteration. Using simulations we show that the modified OMP improves theperformance.