Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

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.&nbsp;

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Measurement Science and Technology

Sparsity driven deterministic sampling strategy for coded aperture X-ray Computed Tomography

Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For a unit norm frame, the absolute value of the cosine of the minimum frame angle is also known as coherence. Two frames are equivalent if one can be obtained from the other via left action of an invertible linear operator. Frame angles can change under the action of a linear operator. Most of the existing works solve different optimization problems to find an optimal linear operator that maximizes the minimal frame angle (in other words, minimizes the coherence). In the present work, nevertheless, we consider the question: Is it always possible to find an equivalent frame with smaller coherence for a given frame?. In this paper, we derive properties of the initial unit norm frame that can ensure an equivalent frame with strictly larger minimal frame angle compared to the initial one. It turns out that the nullspace property of a certain matrix obtained from the initial frame can guarantee such an equivalent frame. We also present the numerical results that support our theoretical claims.

Fulltext

IEEE Signal Processing Letters

Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators

Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a natural sparsity, one can directly employ compressive sensing (CS) techniques to reconstruct the CT images. In CS, sensing matrices having low coherence (a measure providing correlation among columns) provide better image reconstruction. However, the sensing matrix constructed through the incomplete angular set of Radon projections typically possesses large coherence. In this paper, we attempt to reduce the coherence of the sensing matrix via a square and invertible preconditioner possessing a small condition number, which is obtained through a convex optimization technique. The stated properties of our preconditioner imply that it can be used effectively even in noisy cases. We demonstrate empirically that the preconditioned sensing matrix yields better signal recovery than the original sensing matrix. © 2018, Korean Society for Computational and Applied Mathematics.

World University root node

Journal of Applied Mathematics and Computing

Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix

A frame is called scalable, if there exists nonnegative scalars such that column weighted frame is tight. A scaling is called a minimal scaling if it does not contain a proper subscaling. We call a minimal scaling as a sparsest minimal if the cardinality of the support of the scaling is minimal. The objective of the present work is to find a sparsest minimal scaling. We also discuss the uniqueness of sparsest minimal scaled frames as a good candidate for incoherent tight frames in recovering sparse signals. © 2018 IEEE.

2018 IEEE 3rd International Conference on Signal and Image Processing, ICSIP 2018

Incoherent minimal scaled frame

X-ray computed tomography (CT) is one of the most widely used imaging modalities for diagnostic tasks in the clinical application. As X-ray dosage given to the patient has potential to induce undesirable clinical consequences, there is a need for reduction in dosage while maintaining good quality in reconstruction. The present work attempts to address low-dose tomography via an optimization method. In particular, we formulate the reconstruction problem in the form of a matrix system involving a binary matrix. We then recover the image deploying the ideas from the emerging field of compressed sensing (CS). Further, we study empirically the radial and angular sampling parameters that result in a binary matrix possessing sparse recovery parameters. The experimental results show that the performance of the proposed binary matrix with reconstruction using TV minimization by Augmented Lagrangian and ALternating direction ALgorithms (TVAL3) gives comparably better results than Wavelet based Orthogonal Matching Pursuit (WOMP) and the Least Squares solution.