Abstract
The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.
Highlights
The reconstruction of an image from the projection data in tomography by algebraic approaches involves solving a linear system Ax b, (1)where the coefficient matrix A Rm n is determined by the scanning geometry and directions, vector b Rm the projection data obtained from computed tomograpgy (CT) scan and the unknown vector x Rn the image to be reconstructed
The block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework
In order to test the performance of our algorithms in reconstructing images, we implemented algorithms BCAVCS and BDROPCS in Matlab
Summary
Where the coefficient matrix A Rm n is determined by the scanning geometry and directions, vector b Rm the projection data obtained from computed tomograpgy (CT) scan and the unknown vector x Rn the image to be reconstructed. We seek for a solution such that it recovers the original image as good as possible Under the condition that the gradients are sparse enough, the solution of the l1-norm minimization problem (4) is unique and it gives an exact recovery of the image based on compressed sensing theory [8,10]. A block cyclic projection for compressed sensing based tomograph (BCPCS) for solving (4) was proposed [14]. The block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms, under a certain condition for example in the strip-based projection model [16], is derived. Examples are given to illustrate their convergence behavior and noise performance
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