TY - CHAP
T1 - Sparsity-aware Bayesian inference and its applications
AU - Joseph, Geethu
AU - Khanna, Saurabh
AU - Murthy, Chandra R.
AU - Prasad, Ranjitha
AU - Thoota, Sai Subramanyam
PY - 2022
Y1 - 2022
N2 - The emergence of compressive sensing and the associated ℓ1 recovery algorithms and theory have generated considerable excitement and interest in their applications. This chapter will examine recent developments and a complementary set of tools based on a Bayesian framework to address the general problem of sparse signal recovery and the challenges associated with it. Bayesian methods offer superior performance compared to convex optimization-based methods and are parameter tuning-free. They also have the flexibility necessary to deal with a diverse range of measurement modalities and structured sparsity in signals than hitherto possible. Parsimonious signal representation using overcomplete dictionaries for compression, estimation of sparse communication channels with large delay spread as in underwater acoustics, low-dimensional representation of MIMO wireless channels, brain imaging techniques, such as MEG and EEG, are a few examples. We provide a mathematically rigorous and in-depth overview of this fascinating area within sparse signal recovery. We highlight the generality and flexibility of Bayesian approaches and show how it greatly facilitates their deployment in communications-related applications, even though they generally lead to nonconvex optimization problems. Further, we show that, by reinterpreting the Bayesian cost function as a technique to perform covariance matching, one can develop new, ultrafast Bayesian algorithms for sparse signal recovery. As an example application, we discuss the utility of these algorithms in the context of 5G communications with several case studies including wideband time-varying channel estimation and low-resolution analog-to-digital conversion-based signal recovery.
AB - The emergence of compressive sensing and the associated ℓ1 recovery algorithms and theory have generated considerable excitement and interest in their applications. This chapter will examine recent developments and a complementary set of tools based on a Bayesian framework to address the general problem of sparse signal recovery and the challenges associated with it. Bayesian methods offer superior performance compared to convex optimization-based methods and are parameter tuning-free. They also have the flexibility necessary to deal with a diverse range of measurement modalities and structured sparsity in signals than hitherto possible. Parsimonious signal representation using overcomplete dictionaries for compression, estimation of sparse communication channels with large delay spread as in underwater acoustics, low-dimensional representation of MIMO wireless channels, brain imaging techniques, such as MEG and EEG, are a few examples. We provide a mathematically rigorous and in-depth overview of this fascinating area within sparse signal recovery. We highlight the generality and flexibility of Bayesian approaches and show how it greatly facilitates their deployment in communications-related applications, even though they generally lead to nonconvex optimization problems. Further, we show that, by reinterpreting the Bayesian cost function as a technique to perform covariance matching, one can develop new, ultrafast Bayesian algorithms for sparse signal recovery. As an example application, we discuss the utility of these algorithms in the context of 5G communications with several case studies including wideband time-varying channel estimation and low-resolution analog-to-digital conversion-based signal recovery.
KW - Bayesian inference
KW - Covariance matching
KW - Dictionary learning
KW - Quantized compressed sensing
KW - Sparse Bayesian learning
KW - Structured sparsity
KW - Wireless channel estimation
UR - http://www.scopus.com/inward/record.url?scp=85138592896&partnerID=8YFLogxK
U2 - 10.1016/bs.host.2022.07.003
DO - 10.1016/bs.host.2022.07.003
M3 - Chapter
AN - SCOPUS:85138592896
SN - 9780323952682
T3 - Handbook of Statistics
SP - 161
EP - 207
BT - Handbook of Statistics
A2 - Srinivasa Rao, Arni S.R.
A2 - Young, G. Alastair
A2 - Rao, C.R.
PB - Elsevier
ER -