Subspace Constrained Variational Bayesian Inference for Structured Compressive Sensing with a Dynamic Grid
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911965562011648 |
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| author | Liu, An Zhou, Yufan Xu, Wenkang |
| author_facet | Liu, An Zhou, Yufan Xu, Wenkang |
| contents | We investigate the problem of recovering a structured sparse signal from a linear observation model with an uncertain dynamic grid in the sensing matrix. The state-of-the-art expectation maximization based compressed sensing (EM-CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have a relatively slow convergence speed due to the double-loop iterations between the E-step and M-step. Moreover, each inner iteration in the E-step involves a high-dimensional matrix inverse in general, which is unacceptable for problems with large signal dimensions or real-time calculation requirements. Although there are some attempts to avoid the high-dimensional matrix inverse by majorization minimization, the convergence speed and accuracy are often sacrificed. To better address this problem, we propose an alternating estimation framework based on a novel subspace constrained VBI (SC-VBI) method, in which the high-dimensional matrix inverse is replaced by a low-dimensional subspace constrained matrix inverse (with the dimension equal to the sparsity level). We further prove the convergence of the SC-VBI to a stationary solution of the Kullback-Leibler divergence minimization problem. Simulations demonstrate that the proposed SC-VBI algorithm can achieve a much better tradeoff between complexity per iteration, convergence speed, and performance compared to the state-of-the-art algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subspace Constrained Variational Bayesian Inference for Structured Compressive Sensing with a Dynamic Grid Liu, An Zhou, Yufan Xu, Wenkang Signal Processing We investigate the problem of recovering a structured sparse signal from a linear observation model with an uncertain dynamic grid in the sensing matrix. The state-of-the-art expectation maximization based compressed sensing (EM-CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have a relatively slow convergence speed due to the double-loop iterations between the E-step and M-step. Moreover, each inner iteration in the E-step involves a high-dimensional matrix inverse in general, which is unacceptable for problems with large signal dimensions or real-time calculation requirements. Although there are some attempts to avoid the high-dimensional matrix inverse by majorization minimization, the convergence speed and accuracy are often sacrificed. To better address this problem, we propose an alternating estimation framework based on a novel subspace constrained VBI (SC-VBI) method, in which the high-dimensional matrix inverse is replaced by a low-dimensional subspace constrained matrix inverse (with the dimension equal to the sparsity level). We further prove the convergence of the SC-VBI to a stationary solution of the Kullback-Leibler divergence minimization problem. Simulations demonstrate that the proposed SC-VBI algorithm can achieve a much better tradeoff between complexity per iteration, convergence speed, and performance compared to the state-of-the-art algorithms. |
| title | Subspace Constrained Variational Bayesian Inference for Structured Compressive Sensing with a Dynamic Grid |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2407.16947 |