Subspace Aware Recovery of Low Rank and Jointly Sparse Signals

Biswas, Sampurna; Dasgupta, Soura; Mudumbai, Raghuraman; Jacob, Mathews

doi:10.1109/tci.2016.2628352

Cited by 3 publications

(10 citation statements)

References 36 publications

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“…In order to reduce the computational complexity of low-rank matrix reconstruction, the works in [12,13] have proposed adaptive matrix sensing techniques. Specifically, in stead of manipulating the whole observations y in (2), they process the partial observations in two stages,…”

Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

“…In the first stage, y 1 = A 1 (L) + n 1 is taken to estimate the column subspace of the L, which we denote F ∈ R M ×r . The second part y 2 = A 2 (L) + n 2 is to estimate the coefficient matrix with respect to the estimated F in order to reconstruct L. Each technique in [12,13] proposes a method of generating A 2 (·) in (5). In particular, in [12], the elements in A 2 (·) are drawn from i.i.d.…”

Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

“…Since y 1 and y 2 are of much smaller number than p, [12,13] provide the ways to utilize the subspace information to assist the reconstruction of L, and reduce the computational complexity as well. However, these techniques did not fully consider the design of affine maps (A 1 (·), A 2 (·)) and the optimal representation of the estimated low-rank matrix, which can potentially improve the reconstruction accuracy.…”

Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

“…Because of this, it has been widely employed [3,6,14,4,5]. Under the RIP, many of the state of the art reconstruction methods [3,4,5,6,10,11,12,13] employ randomly generated affine maps and focus on the reconstruction algorithms. On the other hand, if one can optimize the affine map to lower reconstruction error of a specific algorithm, it is expected that this will reduce the observation overhead.…”

Section: Motivationmentioning

confidence: 99%

“…Recent work has studied adaptive low-rank matrix reconstruction techniques [12,13] that significantly reduce the computational complexity as well as enhance the reconstruction accuracy. Unlike the non-adaptive approaches [3,4,5,6,7,8,9] where they exploit the entire observations A(L) for reconstruction, the methods proposed in [12,13] divide the reconstruction task into two steps, where each step only needs to manipulate partial observations of A(L) to obtain partial information of L. Considering that the dimension of partial observations is much smaller than the entire observations, the computational complexity can be reduced substantially. An interesting observation is that any partial information of matrix subspace provides a significant clue when adapting the affine map to enhance the reconstruction accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Leveraging subspace information for low-rank matrix reconstruction

et al. 2019

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The problem of low-rank matrix reconstruction arises in various applications in communications and signal processing. The state of the art research largely focuses on the recovery techniques that utilize affine maps satisfying the restricted isometry property (RIP). However, the affine map design and reconstruction under a priori information, i.e., column or row subspace information, has not been thoroughly investigated. To this end, we present designs of affine maps and reconstruction algorithms that fully exploit the low-rank matrix subspace information. Compared to the randomly generated affine map, the proposed affine map design permits an enhanced reconstruction. In addition, we derive an optimal representation of low-rank matrices, which is exploited to optimize the rank and subspace of the estimate by adapting them to the noise level in order to achieve the minimum mean square error (MSE). Moreover, in the case when the subspace information is not a priori available, we propose a two-step algorithm, where, in the first step, it estimates the column subspace of a low-rank matrix, and in the second step, it exploits the estimated information to complete the reconstruction. The simulation results show that the proposed algorithm achieves robust performance with much lower complexity than existing reconstruction algorithms.

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Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

Section: Previous Work: Adaptive Techniquesmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Leveraging subspace information for low-rank matrix reconstruction

et al. 2019

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A Probabilistic Model-Based Method With Nonlocal Filtering for Robust Magnetic Resonance Imaging Reconstruction

2020

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Existing model-based or data-driven methods have achieved a high-quality reconstruction in compressive sensing magnetic resonance imaging (CS-MRI). However, most methods are designed for a specific type of sampling mask or sampling rate while ignoring the existence of external noise, resulting in poor robustness. In this work, we propose a probabilistic model-based method based on Laplacian scale mixture (LSM) modeling and denoising based approximate message passing (D-AMP) algorithm to address this issue. Sparse coefficients of similar packed patches are modeled with LSM distribution to exploit the nonlocal self-similarity prior of MR image, and a maximum a posterior estimation problem for sparse coding is formulated. It is shown that both hidden scale parameters i.e. variances of sparse coefficients and location parameters can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. Moreover, the variance of noise is also iteratively updated based on maximum likelihood estimation. With plug-and-play prior method, the above structured sparse coding procedure can be regarded as a nonlocal filtering operation and be incorporated into DAMP for MR image reconstruction. Owing to the power of our nonlocal filtering which takes both signal and noise estimation into account, the proposed method not only outperforms many state-of-the-art methods for most situations of observation, but also delivers the best qualitative reconstruction results with finer details and less artifacts in experiments. INDEX TERMS Compressive sensing magnetic resonance imaging (CS-MRI), Laplacian scale mixture (LSM), denoising based approximate message passing (D-AMP), nonlocal filtering.

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Reconstructing Video of Time-Varying Sources From Radio Interferometric Measurements

Bouman

Johnson

Dalca

et al. 2018

IEEE Trans. Comput. Imaging

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Very long baseline interferometry (VLBI) makes it possible to recover images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wavelengths with a goal of achieving angular resolution sufficient for imaging the event horizons of nearby supermassive black holes. VLBI provides measurements related to the underlying source image through a sparse set spatial frequencies. An image can then be recovered from these measurements by making assumptions about the underlying image. One of the most important assumptions made by conventional imaging methods is that over the course of a night's observation the image is static. However, for quickly evolving sources, such as the galactic center's supermassive black hole (SgrA*) targeted by the EHT, this assumption is violated and these conventional imaging approaches fail. In this work we propose a new way to model VLBI measurements that allows us to recover both the appearance and dynamics of an evolving source by reconstructing a video rather than a static image. By modeling VLBI measurements using a Gaussian Markov Model, we are able to propagate information across observations in time to reconstruct a video, while simultaneously learning about the dynamics of the source's emission region. We demonstrate our proposed Expectation-Maximization (EM) algorithm, StarWarps, on realistic synthetic observations of black holes, and show how it substantially improves results compared to conventional imaging algorithms. Additionally, we demonstrate StarWarps on real VLBI data of the M87 Jet from the VLBA.

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Subspace Aware Recovery of Low Rank and Jointly Sparse Signals

Cited by 3 publications

References 36 publications

Leveraging subspace information for low-rank matrix reconstruction

Leveraging subspace information for low-rank matrix reconstruction

A Probabilistic Model-Based Method With Nonlocal Filtering for Robust Magnetic Resonance Imaging Reconstruction

Reconstructing Video of Time-Varying Sources From Radio Interferometric Measurements

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