Unification of compressed imaging techniques in the microwave range and deconvolution strategy

Abstract

In recent years, several techniques of imaging have emerged based on compressive sensing. Thus, using passive devices able to code and sum the information measured on a radiating aperture, complex UWB beamforming hardwares can be replaced by inverse problems to solve using deconvolution techniques. Two similar compressive techniques have been developed independently, based on a passive multiplexer and on a metamaterial aperture. This paper proposes an unification of these approaches, using a common mathematical formulation and comparing the deconvolution strategy adopted by each research team.

Computational polarimetric microwave imaging

“…where E t,r (r, ν) + is the pseudo-inverse computed for each independent polarization state on the discrete representation of the radiated fields in transmission and reception [49][50][51], determined from Eqs. (12) and (13) and assuming that the tangential field E tan t,r (r, ν) can be determined from an analytical model (or measured).…”

Synthetic aperture interferometric imaging using a passive microwave coding device

“…This technique was based on the time reversal principle and exploit the frequency diversity of a reverberant cell. It was then extended and applied to SIMO an MIMO imaging [4]- [10]- [11]. Herein, this method is adapted to the SAIR imaging.…”

Sparsity-Driven Reconstruction Technique for Microwave/Millimeter-Wave Computational Imaging

“…Connections can also be made with earlier systems based on the use of frequency scanning antennas whose radiation patterns can encode a sum of information relative to the position of a target into a reduced number of signals [ 20 , 21 , 22 ]. It is necessary to study all these systems in order to analyze them by means of a unified formalism taking into account the propagation of signals, their filtering within dispersive components, and their summation, as described in [ 23 ] and Figure 1 .…”

“…This approach is undoubtedly the simplest and so far the most accurate way of reconstructing an estimation by solving the inverse problem through, for example, a pseudo-inversion: or through iterative reconstruction techniques, exploiting for example prior knowledge on the inherent sparsity of the interrogated scene [ 24 , 25 , 26 , 27 ]. Although this approach is particularly precise and simple to implement, it can suffer from prohibitive memory consumption and computing time, imposing great constraints on the processing units implemented in this framework [ 23 ]. Alternative approaches proposed in previous work explored the possibility of breaking down the M measurement matrix into two operators of reduced dimensions, reconstructing in this context an estimate of the signals in the radiating aperture [ 11 , 12 , 28 ].…”

“…Although independent signal equalization estimation cannot be ideal due to the ratio of the number of measured points to that of unknowns, the coherence of frequency content during the backpropagation operation represented by yields satisfactory results in various applications [ 12 , 13 ]. The distortions observed during the use of this method are counterbalanced by the great gain in calculation time compared to the sensing matrix approach, realized by reducing the dimensions of the problem and replacing the matrix operator by range migration algorithms based on fast Fourier transforms [ 23 ].…”