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- Hema Kumari Achanta, Sampurna Biswas, Soura Dasgupta, Mathews Jacob, Bhanumati N. Dasgupta, Raghuraman Mudumbai
- 2014 IEEE 8th Sensor Array and Multichannel…
- 2014

This paper considers the spark of L × N submatrices of the N × N Discrete Fourier Transform (DFT) matrix. Here a matrix has spark m if every collection of its m - 1 columns are linearly independent. The motivation comes from such applications of compressed sensing as MRI and synthetic aperture radar, where device physics dictates the… (More)

- Greg Ongie, Sampurna Biswas, Mathews Jacob
- 2016 IEEE International Conference on Image…
- 2016

We derive theoretical guarantees for the exact recovery of piecewise constant two-dimensional images from a minimal number of non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities of the image are localized to the zero level-set of a bandlimited function, which induces certain linear dependencies in Fourier… (More)

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of the matrix is solved using a simple… (More)

- Sampurna Biswas, Hema Kumari Achanta, Mathews Jacob, Soura Dasgupta, Raghuraman Mudumbai
- IEEE Signal Processing Letters
- 2015

We provide a two-step approach to recover a jointly k-sparse matrix X, (at most k rows of X 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 X, the proposed algorithm comprises two stages, in each of which the measurement is taken by… (More)

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… (More)

- Sampurna Biswas, Soura Dasgupta, Mathews Jacob, Raghuraman Mudumbai
- 2015 23rd European Signal Processing Conference…
- 2015

We consider the spark of submatrices of 2D-DFT matrices obtained by removing certain rows and relate it to the spark of associated 1D-DFT submatrices. A matrix has spark m if its smallest number of linearly dependent columns equals m. To recover an arbitrary fc-sparse vector, the spark of an observation matrix must exceed 2fc. We consider how to choose the… (More)

- Hema Kumari Achanta, Sampurna Biswas, Bhanumati N. Dasgupta, Soura Dasgupta, Mathews Jacob, Raghuraman Mudumbai
- Digital Signal Processing
- 2017

- Sampurna Biswas, Soura Dasgupta, Raghuraman Mudumbai, Mathews Jacob
- IEEE Transactions on Computational Imaging
- 2017

We consider the recovery of a matrix <inline-formula><tex-math notation="LaTeX">${\mathbf X}$</tex-math> </inline-formula>, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Each column of <inline-formula><tex-math notation="LaTeX">${\mathbf X}$</tex-math></inline-formula> is measured using a… (More)

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… (More)

- Greg Ongie, Sampurna Biswas, Mathews Jacob
- ArXiv
- 2017

—We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero level-set of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image,… (More)

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