This repository contains demos that show how to solve 2D and 3D constrained Total Variaton image reconstruction problems using the Split Bregman formulation.
TV_SB_2D.m and TV_SB_3D.m solve the constrained total variation problem
where A is a linear operator (a matrix) that projects the image u to the data f. The code works for general linear inverse problems. It currently expects A to be a matrix; it can be easily modified to use A as a MATLAB function by changing A and A' for functions that compute forward and adjoint operations.
These demos solve the compressed sensing problem for magnetic resonance imaging as an exemplar. A is the Fourier transform provided as a matrix operator, f is undersampled data, and u is a 2D image.
The repository contains the following files:
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Demo_TV_SB_2D.m: Demo for 2D TV reconstruction
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Demo_TV_SB_3D.m: Demo for 3D TV reconstruction
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TV_SB_2D.m: 2D TV reconstruction
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TV_SB_3D.m: 3D TV reconstruction
If you use this code, please, cite the following paper: Abascal JF, Chamorro-Servent J, Aguirre J, Arridge S, Correia T, Ripoll J, Vaquero JJ, Desco M. Fluorescence diffuse optical tomography using the split Bregman method. Med Phys. 38(11):6275-84, 2011. DOI: http://dx.doi.org/10.1118/1.3656063
If you need to contact the author, please do so at juanabascal78@gmail.com, juchamser@gmail.com, desco@hggm.es