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of the Dissertation Fast and Robust Algorithms for Compressive Sensing and Other Applications

Background Compressed sensing (CS) based myocardial perfusion MRI methods that promote sparsity in temporal transform domains such as temporal Fourier (x-f), temporal PCA (x-PCA), temporal total variation (x-TV) have shown promise to accelerate breath held scans [Otazo et al, 10, Pedersen et al, 09, Adluru et al, 07]. However the performances of these schemes can degrade in the presence of moti...

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of an minimum mean square error (MMSE) estimator that has support knowledge beyond a certain SNR thredhold. The key idea behind CS-BSD is that reconstruction takes a dete...

Article history: Available online 2 October 2013

The principle of compressed sensing (CS) can be applied in a cryptosystem by providing the notion of security. In information-theoretic sense, it is known that a CS-based cryptosystem can be perfectly secure if it employs a random Gaussian sensing matrix updated at each encryption and its plaintext has constant energy. In this paper, we propose a new CS-based cryptosystem that employs a secret ...

Abstract—This paper provides clustered compressive sensing (CCS) based image processing using Bayesian framework applied to medical images. Some images, for example like magnetic resonance images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. Compressed sensing (CS) paradigm can be applied in order to boost such signals. We applied CS p...

Compressed sensing (CS), a reconstruction method for undersampled MR data, was recently introduced [1]. Since only undersampled data are acquired, CS allows a significant reduction in the time needed for MR experiments. The basic requirement for CS, however, is sparsity in the data. The lack of F background signal in living tissue leads to an intrinsically sparse signal distribution in the F im...

Compressed sensing (CS) can recover sparse signals from undersampled measurements. In this work, we have developed an advanced CS framework for photoacoustic computed tomography (PACT). During the reconstruction, a small part of the nonzero signals’ locations in the transformed sparse domain is used as partially known support (PKS). PACT reconstructions have been performed with under-sampled in...