Multifrequency Bayesian compressive sensing methods for microwave imaging

Lorenzo Poli; Giacomo Oliveri; Ping Ping Ding; Toshifumi Moriyama; Andrea Massa

doi:10.1364/JOSAA.31.002415

Journal of the Optical Society of America A
Vol. 31,
Issue 11,
pp. 2415-2428
(2014)
•https://doi.org/10.1364/JOSAA.31.002415

Multifrequency Bayesian compressive sensing methods for microwave imaging

Lorenzo Poli, Giacomo Oliveri, Ping Ping Ding, Toshifumi Moriyama, and Andrea Massa

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Lorenzo Poli, Giacomo Oliveri, Ping Ping Ding, Toshifumi Moriyama, and Andrea Massa, "Multifrequency Bayesian compressive sensing methods for microwave imaging," J. Opt. Soc. Am. A 31, 2415-2428 (2014)

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Abstract

The Bayesian retrieval of sparse scatterers under multifrequency transverse magnetic illuminations is addressed. Two innovative imaging strategies are formulated to process the spectral content of microwave scattering data according to either a frequency-hopping multistep scheme or a multifrequency one-shot scheme. To solve the associated inverse problems, customized implementations of single-task and multitask Bayesian compressive sensing are introduced. A set of representative numerical results is discussed to assess the effectiveness and the robustness against the noise of the proposed techniques also in comparison with some state-of-the-art deterministic strategies.

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	MF-MT-BCS					FH-ST-BCS
SNR (dB)	$ξ_{tot}$	$ξ_{int}$	$ξ_{ext}$	$Δ t$ [s]	$ξ_{tot}$	$ξ_{int}$	$ξ_{ext}$	$Δ t$ [s]
50	$3.15 \times 10^{- 3}$	$5.42 \times 10^{- 2}$	$8.01 \times 10^{- 4}$	9.97	$1.61 \times 10^{- 2}$	$2.81 \times 10^{- 1}$	$5.02 \times 10^{- 3}$	$3.04 \times 10^{1}$
20	$6.27 \times 10^{- 3}$	$8.14 \times 10^{- 2}$	$2.25 \times 10^{- 3}$	8.92	$1.60 \times 10^{- 2}$	$2.71 \times 10^{- 1}$	$5.17 \times 10^{- 3}$	$3.07 \times 10^{1}$
10	$7.19 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	$2.35 \times 10^{- 3}$	9.21	$2.09 \times 10^{- 2}$	$3.21 \times 10^{- 1}$	$8.80 \times 10^{- 3}$	$3.02 \times 10^{1}$
5	$2.01 \times 10^{- 2}$	$2.55 \times 10^{- 2}$	$8.49 \times 10^{- 3}$	9.75	$3.49 \times 10^{- 2}$	$3.77 \times 10^{- 1}$	$1.83 \times 10^{- 2}$	$3.12 \times 10^{1}$

	SNR
$τ$	20 dB	10 dB	5 dB
1.0	$3.36 \times 10^{- 3}$	$3.50 \times 10^{- 3}$	$3.88 \times 10^{- 3}$
2.0	$4.73 \times 10^{- 3}$	$4.03 \times 10^{- 3}$	$3.30 \times 10^{- 3}$
3.0	$3.15 \times 10^{- 3}$	$3.03 \times 10^{- 3}$	$4.42 \times 10^{- 3}$

	MF-MT-BCS					FH-ST-BCS
SNR (dB)	$ξ_{tot}$	$ξ_{int}$	$ξ_{ext}$	$Δ t$ [s]	$ξ_{tot}$	$ξ_{int}$	$ξ_{ext}$	$Δ t$ [s]
50	$3.15 \times 10^{- 3}$	$5.42 \times 10^{- 2}$	$8.01 \times 10^{- 4}$	9.97	$1.61 \times 10^{- 2}$	$2.81 \times 10^{- 1}$	$5.02 \times 10^{- 3}$	$3.04 \times 10^{1}$
20	$6.27 \times 10^{- 3}$	$8.14 \times 10^{- 2}$	$2.25 \times 10^{- 3}$	8.92	$1.60 \times 10^{- 2}$	$2.71 \times 10^{- 1}$	$5.17 \times 10^{- 3}$	$3.07 \times 10^{1}$
10	$7.19 \times 10^{- 3}$	$1.09 \times 10^{- 1}$	$2.35 \times 10^{- 3}$	9.21	$2.09 \times 10^{- 2}$	$3.21 \times 10^{- 1}$	$8.80 \times 10^{- 3}$	$3.02 \times 10^{1}$
5	$2.01 \times 10^{- 2}$	$2.55 \times 10^{- 2}$	$8.49 \times 10^{- 3}$	9.75	$3.49 \times 10^{- 2}$	$3.77 \times 10^{- 1}$	$1.83 \times 10^{- 2}$	$3.12 \times 10^{1}$

	SNR
$τ$	20 dB	10 dB	5 dB
1.0	$3.36 \times 10^{- 3}$	$3.50 \times 10^{- 3}$	$3.88 \times 10^{- 3}$
2.0	$4.73 \times 10^{- 3}$	$4.03 \times 10^{- 3}$	$3.30 \times 10^{- 3}$
3.0	$3.15 \times 10^{- 3}$	$3.03 \times 10^{- 3}$	$4.42 \times 10^{- 3}$

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Equations (20)

Journal of the Optical Society of America A