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Case Western Reserve University DEPARTMENT OF MATHEMATICS |
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DEPARTMENT OF MATHEMATICS SEMINARS and COLLOQUIAImaging |
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Jing QIN Graduate Student Department of Mathematics Case Western Reserve University "Compressive Sensing Reconstruction Based on High Frequency Subbands and Weighted TV Sparsity" Date: Wednesday, May 2, 2012 Time: 2:00-3:00 p.m. Location: CWRU Department of Mathematics Yost Hall - Room 300 ABSTRACT In compressive sensing, accurate image reconstruction from very few noisy linear projection is challenging, especially for natural images containing a lot of detail. The success of compressive sensing reconstruction lies in appropriate selection of sparsifying transform and numerical reconstruction algorithm. We choose to use shearlet transform that is recently proven to be mathematically optimal in encoding images with anisotropic features such as edges, corners, junctions and spikes. But instead of common procedure of enforcing all subbands to be sparse, we only use high frequency subbands to maximize the sparsity and thereby reduce the required sampling rate. To better reconstruct fine features, we also add weighted TV sparsity. The model is implemented using alternating direction method (ADM). Through introducing auxiliary variables, at each iteration, it solves three subproblems that have closed form. The convergence of the ADM algorithm is readily proved and the efficiency and stability of numerical results show that our proposed method recovers the features and textures better than the existing methods.
Jing QIN
ABSTRACT Prior information of image, including geometric prior and local/global image regularities, plays an important role in image processing and compressive sensing(CS). In this talk, we will discuss how to incorporate image prior into image denoising and image reconstruction to enhance the performance significantly. CS reconstructs an image with fewer measurements required by Shannon-Nyquist sampling theorem. We will present a novel two-stage method called GeoCS using the pixel-to-pixel varying weights associated to the total variation. Due to its optimality in representing anisotropic image features, shearlet transform is employed in our model as sparsifying frame. The model is solved efficiently by applying split Bregman algorithm. By incorporating global image smoothness prior, we recently developed one total generalized variation (TGV) based image reconstruction model. Various numerical results show the greater benefits of prior information in image reconstruction even as the sampling rate goes lower. Effectiveness of edge information in boosting image denoising from images with excessive inhomogeneous noise and artifacts will also be mentioned in NL-means framework.
Case Western Reserve University |
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