Publication: Quantitative signal subspace imaging
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2021-12
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IOP Science
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Abstract
We develop and analyze a quantitative signal subspace imaging method for single-frequency array imaging. This method is an extension to multiple signal classification which uses (i) the noise subspace to determine the location and support of targets, and (ii) the signal subspace to recover quantitative information about the targets. For point targets, we are able to recover the complex reflectivity and for an extended target under the Born approximation, we are able to recover a scalar quantity that is related to the product of the volume and relative dielectric permittivity of the target. Our resolution analysis for a point target demonstrates this method is capable of achieving exact recovery of the complex reflectivity at subwavelength resolution. Additionally, this resolution analysis shows that noise in the data effectively acts as a regularization to the imaging functional resulting in a method that is surprisingly more robust and effective with noise than without noise.
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Corrigendum: Quantitative signal subspace imaging (2021 Inverse Problems 37 125006). Inverse Problems, 38(4), 049501. https://doi.org/10.1088/1361-6420/ac509e
In the numerical results of [1], the reported signal-to-noise ratios (SNRs) are incorrect. We give the correct SNR values below. For the results shown in figure 2 and corresponding discussion, SNR = 45.334 dB. For the results shown in figure 7 and corresponding discussion, SNR = 55.146 dB. For the results shown in figure 9 and corresponding discussion, SNR = 45.387 dB. For the results shown in figure 10 and corresponding discussion, SNR = 105.172 dB. For the results shown in figure 11 and corresponding discussion, SNR = 105.172 dB for figure 11(b), SNR = 55.247 dB for figure 11(c), and SNR = 25.211 dB for figure 11(d).
In the numerical results of [1], the reported signal-to-noise ratios (SNRs) are incorrect. We give the correct SNR values below. For the results shown in figure 2 and corresponding discussion, SNR = 45.334 dB. For the results shown in figure 7 and corresponding discussion, SNR = 55.146 dB. For the results shown in figure 9 and corresponding discussion, SNR = 45.387 dB. For the results shown in figure 10 and corresponding discussion, SNR = 105.172 dB. For the results shown in figure 11 and corresponding discussion, SNR = 105.172 dB for figure 11(b), SNR = 55.247 dB for figure 11(c), and SNR = 25.211 dB for figure 11(d).
Keywords
Multiple signal classification, Linear sampling, Factorization method, Quantitative array imaging
Bibliographic citation
González-RodrĂguez, P., Kim, A. D., & Tsogka, C. (2021). Quantitative signal subspace imaging. Inverse Problems, 37(12), 125006.