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Biswas S.,University Iowa | Poddar S.,University Iowa | Dasgupta S.,University Iowa | Mudumbai R.,University Iowa | Jacob M.,University Iowa
Conference Record - Asilomar Conference on Signals, Systems and Computers | Year: 2015

We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of the matrix corresponds to a frame in the image time series; the matrix is highly low-rank since the frames are highly correlated. Similarly the non-zero locations of the matrix in appropriate transform/frame domains (e.g. wavelet, gradient) are roughly the same in different frame. The superset of the support can be safely assumed to be jointly sparse. Unlike the classical multiple measurement vector (MMV) setup that measures all the snapshots using the same matrix, we consider each snapshot to be measured using a different measurement matrix. We show that this approach reduces the total number of measurements, especially when the rank of the matrix is much smaller than than its sparsity. Our experiments in the context of dynamic imaging shows that this approach is very useful in realizing free breathing cardiac MRI. © 2014 IEEE.

Haug J.,University Iowa | Goguri S.,University Iowa | Mudumbai R.,University Iowa | Dasgupta S.,University Iowa
Chinese Control Conference, CCC | Year: 2015

We present a class of nonlinear observers that track oscillator states from observations of the complex envelope. We first identify core state variables that are observable and provide a general observer structure for estimating these state variables, that results in globally uniformly asymptotically stable observers. We provide a specialization that induces the 2-norm of the state estimation error to monotonically decline to zero, and has an intuitively appealing structure that has parallels to full order observers of Linear Time Invariant systems. © 2015 Technical Committee on Control Theory, Chinese Association of Automation.

Biswas S.,University Iowa | Achanta H.K.,University Iowa | Jacob M.,University Iowa | Dasgupta S.,University Iowa | Mudumbai R.,University Iowa
IEEE Signal Processing Letters | Year: 2015

We provide a two-step approach to recover a jointly k-sparse matrix , (at most k rows of are nonzero), with rank r << k from its under sampled measurements. Unlike the classical recovery algorithms that use the same measurement matrix for every column of , the proposed algorithm comprises two stages, in each of which the measurement is taken by a different measurement matrix.The first stage uses a standard algorithm, to recover any r columns (e.g.The first r) of .The second uses a new set of measurements and the subspace estimate provided by these columns to recover the rest. We derive conditions on the second measurement matrix to guarantee perfect subspace aware recovery for two cases: First a worst-case setting that applies to all matrices.The second a generic case that works for almost all matrices. We demonstrate both theoretically and through simulations that when r << k our approach needs far fewer measurements. It compares favorably with recent results using dense linear combinations, that do not use column-wise measurements. © 1994-2012 IEEE.

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