Total Variation (TV) <i>l</i>1 Norm Minimization Based Limited Data X-ray CT Image Reconstruction

Sarkar, Shubhabrata; Wahi, Pankaj; Munshi, P.

doi:10.1080/09349847.2019.1673857

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…In recent years, image reconstruction methods that optimize the sparsity of the CT images in a transformed domain have become popular. As a result, techniques from compressed sensing (CS) as applied to CT image reconstruction have attracted the attention of the research community [10,11,17,19,22,25]. Notwithstanding the potential of CS-based ideas, one, needs to be careful while applying CS techniques to CT image reconstruction because the subsampled Radon sensing matrices can become rank-deficient and ill-conditioned [10,11,17,25].…”

Section: Introductionmentioning

confidence: 99%

“…In [10], the authors established empirically the existence of a critical number of projections required for accurate reconstruction via a total variation (TV)-regularized method, while quantifying how this critical number is tied to the sparsity of underlying images. The authors of [22] proposed an attractive solution to limited data reconstruction in CT from an industrial and engineering perspective by using a minimization technique involving a higher order TV-regularization term and l 2 norm.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sparsity-driven deterministic sampling strategy for coded aperture x-ray computed tomography

Sonkar¹,

Sasmal²,

Theeda³

et al. 2021

Meas. Sci. Technol.

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The subsampling strategies in X-ray Computed Tomography (CT) gained importance due to their practical relevance. In this direction of research, also known as coded aperture X-ray computed tomography (CAXCT), both random and deterministic strategies were proposed in the literature. Of the techniques available, the ones based on Compressive Sensing (CS) recently gained more traction as CS based ideas eﬃciently exploit inherent duplication present in the system. The quality of the reconstructed CT images, nevertheless, depends on the sparse signal recovery properties (SRPs) of the sub-sampled Radon matrices. In the present work, we determine CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the incoherent unit norm tight frames (IUNTFs) for better numerical behaviour. We show that this optimization, via Khatri-Rao product, leads to non-negative sparse approximation. While comparing and contrasting our method with its existing counterparts, we show that the proposed algorithm is computationally less involved. Finally, we demonstrate eﬃcacy of the proposed deterministic sub-sampling strategy in recovering CT images both in noiseless and noisy cases.

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