Tyseer Aboulnasr

Compressed Sensing Based Real-Time Dynamic MRI Reconstruction

This work addresses the problem of real-time online reconstruction of dynamic magnetic resonance imaging sequences. The proposed method reconstructs the difference between the previous and the current image frames. This difference image is sparse. We recover the sparse difference image from its partial k-space scans by using a nonconvex compressed sensing algorithm. As there was no previous fast enough algorithm for real-time reconstruction, we derive a novel algorithm for this purpose. Our proposed method has been compared against state-of-the-art offline and online reconstruction methods. The accuracy of the proposed method is less than offline methods but noticeably higher than the online techniques. For real-time reconstruction we are also concerned about the reconstruction speed. Our method is capable of reconstructing 128 × 128 images at the rate of 6 frames/s, 180 × 180 images at the rate of 5 frames/s and 256 × 256 images at the rate of 2.5 frames/s.

Non-convex algorithm for sparse and low-rank recovery: Application to dynamic MRI reconstruction

In this work we exploit two assumed properties of dynamic MRI in order to reconstruct the images from under-sampled K-space samples. The first property assumes the signal is sparse in the x-f space and the second property assumes the signal is rank-deficient in the x-t space. These assumptions lead to an optimization problem that requires minimizing a combined lp-norm and Schatten-p norm. We propose a novel FOCUSS based approach to solve the optimization problem. Our proposed method is compared with state-of-the-art techniques in dynamic MRI reconstruction. Experimental evaluation carried out on three real datasets shows that for all these datasets, our method yields better reconstruction both in quantitative and qualitative evaluation.

Algorithms to Approximately Solve NP Hard Row-Sparse MMV Recovery Problem: Application to Compressive Color Imaging

This paper addresses the row-sparse multiple measurement vector (MMV) recovery problem. This requires solving a nondeterministic polynomial (NP) hard optimization. Instead of approximating the NP hard problem by its convex/nonconvex surrogates as is done in other studies, we propose techniques to directly solve the NP hard problem approximately with tractable algorithms. The algorithms derived in here yields better recovery rates than the state-of-the-art convex (spectral projected gradient) algorithm we compared against. We show that the compressive color image reconstruction can be formulated as an MMV recovery problem with sparse rows and therefore can be solved by our proposed method. The reconstructed images are more accurate (improvement about 2 dB in peak signal-to-noise ratio) than the previous technique compared against.

A focuss based method for low rank matrix recovery

In this work, we address the problem of low-rank matrix recovery from its under-sampled projections. The recovery is formulated as a Schatten-p norm minimization problem. We proposed a novel algorithm to solve the Schatten-p norm minimization problem based on the FOCUSS (FOCally Under-determined System Solver) approach. We compared our proposed method with state-of-the-art solvers. Experimental evaluation was carried out on two problems - matrix completion and image inpainting. For matrix completion, our proposed method showed better recovery rate than other methods. In the image inpainting problem, our method yields 1.5 dB improvement over the nearest competing algorithm.

A novel reduced power compressive sensing technique for wideband cognitive radio

Wideband spectrum sensing for cognitive radio requires high rate analog to digital (A/D) converters whose power consumption is proportional to the sampling rate. In this article, we propose to use sub-Nyquist non-uniform sampling for spectrum sensing to reduce the power consumption. Since the received signal samples are correlated in the time domain, we estimate the missing samples by using the expectation-maximization (EM) algorithm. It is shown that the combined sub-Nyquist non-uniform sampling and EM algorithm consume much less power than A/D converter at the Nyquist rate making the proposed algorithm a viable low-power solution for spectrum sensing. Moreover, it is shown by simulations that the proposed sub-Nyquist rate non-uniform sampler is accurate enough to detect the edges of the estimated power spectral density.

Simplified DFT: A novel method for wideband spectrum sensing in cognitive radio

Four simplified discrete Fourier transform (SDFT)-based spectrum sensing methods are introduced for power spectral density (PSD) estimation for cognitive radio (CR). The SDFT-based spectrum sensing techniques are less computationally complex than DFT techniques since no multiplications are required in the time-to-frequency domain conversion process. The simulation results and mathematical analyses indicate that the performance of the SDFT-based spectrum sensing method is comparable to that of the DFT-based one when the received signal spectrum is lightly occupied.

Image similarity measurement from sparse reconstruction errors

This paper presents a new approach to measuring the similarity between two images using sparse reconstruction. Our approach alleviates the difficulty of selecting and extracting suitable features from images which usually requires domain-specific knowledge. The proposed measure, the Sparse SNR (SSNR), does not use any prior knowledge about the data type or the application. SSNR is generic in the sense that it is applicable, without modification, to a variety of problems involving different types of images. Given a pair of images, a set of basis vectors (dictionary) is learnt for each image such that each image can be represented as a linear combination of a small number of its dictionary elements. Each image is reconstructed by two dictionaries - the one trained on the image itself and the second - trained on the other image. We develop a novel similarity measure based on the resulting reconstruction errors. To the best of our knowledge, this is the first attempt to develop a sparse reconstruction-based similarity measure. Excellent classification, clustering and retrieval results are achieved on benchmark datasets involving facial images and textures.

A novel multi-resolution based PSD estimation method based on expectation maximization algorithm

Power spectral density (PSD) estimation is used in many applications such as spectrum sensing for cognitive radio (CR). For a fixed number of samples, one must trade-off estimation accuracy against frequency resolution. We propose a multi-resolution method based on the expectation-maximization (EM) algorithm that provides both high frequency resolution and low estimation error variance. First a high resolution PSD estimate with high estimation error variance is produced. Then, from the same set of samples, we produce a low frequency resolution PSD estimate with low estimation error variance. Using information from the first PSD estimate, the EM algorithm is used to estimate the missing frequency bins of the PSD with low frequency resolution. It is shown by analysis and simulation that the proposed method improves both the resolution and estimation error variance compared to conventional PSD estimation.