Abstract
Numerous prototypes of computational imaging systems have recently been presented in the microwave and millimeter-wave domains, enabling the simplification of associated active architectures through the use of radiating cavities and metasurfaces that can multiplex signals encoded in the physical layer. This paper presents a new reconstruction technique leveraging the sparsity of the signals in the time-domain and decomposition of the sensing matrix by support detection, the size of the computational inverse problem being reduced significantly without compromising the image quality.
Highlights
Microwave and millimeter-wave imaging applications are becoming increasingly numerous and cover a wide range of fields such as medical diagnostics [1,2,3,4], non-destructive testing [5,6,7], and concealed weapon detection [8,9,10]
All short-range imaging applications mentioned in the first part of the introduction of this document share interesting characteristics, which are directly exploited by the proposed technique: the targets studied have a limited depth extension and are interrogated with ultra-wideband signals
The compact sensing matrix Ts = ( Ts, ..., Ts) is obtained from the concatenation of truncated Toeplitz matrices computed as follows: Ts = D[tmin,tmax ] diag( H) D[†tρ where H is a frequency-dependent eigenvector of nω samples corresponding to the transfer function of the computational imaging component measured at the location rri of the radiating aperture and the couple of matrices D[tρ,tρmax ] ∈ C nρ ×nω and D[tmin,tmax ] ∈ C ns ×nω are discrete min Fourier transform matrices computed in the bounds of the time-domain values specified in the index
Summary
Microwave and millimeter-wave imaging applications are becoming increasingly numerous and cover a wide range of fields such as medical diagnostics [1,2,3,4], non-destructive testing [5,6,7], and concealed weapon detection [8,9,10]. The principle of computational imaging applied to the microwave and millimeter-wave domains consists in using structured radiation patterns with a low degree of correlation in order to encode the information contained in the target space into electrical signals measured on a reduced number of ports in order to limit the costs and complexity associated with active systems. Nω corresponds to the number of frequency samples and nr to the number of voxels of the discretized target space This relation makes it clear that spatial information is encoded in a frequency signal and that the rank of the sensing matrix—directly related to the pseudo-orthogonality between the radiated patterns at each frequency—is the main limitation of the number of unknowns that can be reconstructed. The theoretical principle, based on the exploitation of sparsity in the time-domain, is presented which is followed by theoretical and experimental studies
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