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.
Prior support constrained compressed sensing, achieved via the weighted norm minimization, has of late become popular due to its potential for applications. For the weighted norm minimization problem, min x p,w subject to y = Ax, p = 0, 1, and w ∈ [0, 1],uniqueness results are known when w = 0, 1. Here, x p,w = w xT p + xT c p , p = 0, 1 with T representing the partial support information. The work reported in this paper presents the conditions that ensure the uniqueness of the solution of this problem for general w ∈ [0, 1].
Prior support constrained compressed sensing has of late become popular due to its potential for applications. The existing results on recovery guarantees provide global recovery bounds in the sense that they deal with full support. However, in some applications, one might be interested in the recovery guarantees limited to the given prior support, such bounds may be termed as local recovery bounds. The present work proposes the local recovery guarantees and analyzes the conditions on associated parameters that make recovery error small.
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