_____ ___ _______ __ __ / ____\ / _ \ |__ __| \ \ / / \____ \ / ___ \ | | \ \/ / /_____/ /_/ \_\ |_| \__/ Spatially Adapted Total Variation (SA-TV) Method (http://www.uni-graz.at/imawww/ifb/sa-tv/index.html) ________________________________________________________________ OVERVIEW The spatially adapted total variation method is based on a multi- scale total variation model for image restoration. The model utilizes a spatially dependent regularization parameter in order to enhance image regions containing details, while still sufficiently smoothing homogeneous features. The fully automated adjustment strategy of the regularization parameter is based on local variance estimators. To speed-up the performance of the update scheme, a generalized hierarchical decomposition of the restored image is used. The corresponding subproblems are solved by a locally superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth-Newton techniques. The SATV Toolbox was written in MATLAB. It implements: 1) image restoration with a scalar regularization parameter for - Gaussian noise removal; - deblurring and Gaussian noise removal; 2) image restoration with a spatially dependent parameter for - Gaussian noise removal; - deblurring and Gaussian noise removal. _________________________________________________________________ REFERENCE For scalar regularization parameter-based solver: [1] M. Hintermueller and G. Stadler, "An Infeasible Primal-Dual Algorithm for Total Bounded Variation-Based Inf-Convolution-Type Image Restoration", SIAM Journal on Scientific Computing, 28(1): 1-23, 2006. For spatially dependent parameter-based solver: [2] Y.Q. Dong, M. Hintermueller and M. M. Rincon-Camacho, "Auto- mated Regularization Parameter Selection in a Multi-Scale Variation Model for Image Restoration", accepted for publication in Journal of Mathematical imaging and vision, IFB-Report No. 22 (11/2008), Institute of Mathematics and Scientific Computing, University of Graz. For color image restoration (which is not yet included in this version of the toolbox) [3] Y.Q. Dong, M. Hintermueller and M. M. Rincon-Camacho, "A Multi- Scale Vectorial L^\tau-TV Framework for Color Image Restoration", International Journal of Computer Vision. DOI: 10.1007/s11263-010-0359-1. _________________________________________________________________ DIRECTORY STRUCTURE main.m Main script for running the SA-TV method. set_parameter.m Script for user-specified parameter selection. Users are able to focus on different aspects in the restoration by selecting specific values of the parameters. input_image.m Function for the input of image data. For exploring the code, users may select the given test image "camaraman.tif"(default). Alternatively, image data may be selected from a menu window. degrade_image.m Function for creating a degraded image. The default setting is a corruption of the test image by 10% white Gaussian noise. primal_dual_method.m Function running the image restoration by the SA-TV method. cameraman.tif Given test image. README.txt This file. @do (dir) Source codes of semismooth Newton solver. @uv (dir) Source codes of semismooth Newton solver. pdmethod (dir) Source codes for solving the multi-scale total variation model. lambdaupdate (dir) Source codes for regularization parameter update (only for a spatially dependent parameter). _________________________________________________________________ ACKNOWLEDGEMENT The SATV method was developed by Y.Q. Dong, M. Hintermueller and M. M. Rincon-Camacho at the Institute of Mathematics and Scientific Computing of the University of Graz, and the Department of Mathematics of the Humboldt-University of Berlin. This work is supported by the Austria Science Fund FWF under START-program Y305 "Interfaces and Free Boundaries" and the SFB F32 "Mathematical Optimization and Applications in Biomedical Sciences". _________________________________________________________________ DISCLAIMER The SATV Toolbox (including code modifications) may only be used for NON-COMMERCIAL RESEARCH purposes. For inquiries concerning a different use, please contact Prof. M. Hintermueller at Humboldt-University of Berlin (hint"at"math.hu-berlin.de). Your comments are welcome. Please keep track of bugs or missing/ confusing instructions and report them to Yiqiu Dong Michael Hintermueller M. Monserrat Rincon-Camacho The algorithms contained in the SATV Toolbox were implemented by Martin Kanitsar (University of Graz) and revised by Yiqiu Dong.