Controlled wavelet domain sparsity for x-ray tomography

Abstract

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point (PDFP) algorithm introduced by Peijun Chen, Jianguo Huang, and Xiaoqun Zhang (Fixed Point Theory and Applications 2016) showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter µ > 0 is analogous to the notoriously difficult problem of picking the optimal regularization parameter in Tikhonov regularization. Here, a novel automatic method is introduced for choosing µ, based on a control algorithm driving the sparsity of the reconstruction to an a priori known ratio of nonzero versus zero wavelet coefficients in the unknown.

Sparse dynamic tomography: a shearlet-based approach for iodine perfusion in plant stems

“…Which one to pick depends on the problem at hand. Here, we apply an automated controlled sparsity scheme, called controlled wavelet domain sparsity (CWDS), first proposed in [37].…”

“…For static tomography, 1 -priors have been widely investigated and were used for the first time on X-ray measurements with real data [45,46]; 1 shearlet-based regularization has been used to investigate numerous limited data problems (e.g., [2] and the references therein) but the use of shearlets for dynamic tomography has never been investigated before. An initial proof of concept for this approach was carried out by the authors in [3], but in this paper we adopt a different minimization algorithm complemented with the sparsity-based automatic choice for the regularization parameter, introduced in [37], which ease the well-known problem of the choice of the regularization parameter. Also, we complement the numerical experiments section with a brief analysis of the proposed approach in the continuous setting, showing the existence of minimizers for the proposed functional.…”

A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images

“…X-ray imaging can also benefit from the advantages of wavelet domain. In [50], Purisha et al, use a controlled orthonormal wavelet domain for the reconstruction of a tomographic image.…”

A Green Prospective for Learned Post-processing in Sparse-view Tomographic Reconstruction

“…Such low-dose tomographic approaches lead to incomplete CT projection data and these subsampled measurements usually produce severe streaking artifacts on the Filtered Back-Projection (FBP) reconstructions. To address this, compressed sensing-based approaches have been investigated in literature, minimizing the Total Variation (TV) or other sparsity-promoting priors combined with data fidelity terms [4][5][6][7][8][9][10][11]. Although the very accurate achievable results, the optimization approach has not been widely adopted yet in clinical setting, for its high computational cost.…”