Abstract
The standard weighted L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm total variation multiplicative regularization (MR) term originally developed for microwave imaging (MWI) algorithms is modified to take into account structural prior information, also known as spatial priors (SPs), about the object being imaged. This modification adds one extra term to the integrand of the standard MR, thus being referred to as an augmented MR (AMR). The main advantage of the proposed approach is that it requires a minimal change to the existing MWI algorithms that are already equipped with the MR. Using two experimental data sets, it is shown that the proposed AMR 1) can handle partial (incomplete) SP and 2) can, to some extent, enhance the quantitative accuracy achievable from MWI.
Highlights
M ICROWAVE imaging (MWI) is a non-invasive imaging method with which quantitative images of the relative complex permittivity profiles of the objects of interest (OI) can be created
We evaluate the performance of augmented MR (AMR)-Gauss-Newton inversion (GNI) and AMR-contrast source inversion (CSI) against two experimental data sets for two-dimensional scalar microwave imaging
The steering parameter δn2, which is a real number, gets smaller as the inversion algorithm gets closer to the final solution. (For the expressions of δn2 in the multiplicative regularization (MR)-GNI and MR-CSI algorithms, see [16] and [17], respectively.) The operation of MR has been described in previous works such as [17]–[19]; we only provide a quick overview
Summary
M ICROWAVE imaging (MWI) is a non-invasive imaging method with which quantitative images of the relative complex permittivity profiles of the objects of interest (OI) can be created. If in a region within the imaging domain, δn is dominant compared to |∇χn(r)|2, the above Laplacian approximation is still valid locally, and the regularization operator attempts to smooth out that region Otherwise, it favours to reconstruct an edge in that region. Given the SP, we can guide the inversion algorithm regarding the locations at which some edges (i.e., the boundaries between different regions) are to be expected To this end, we rely on the relative magnitude of |∇χn(r)|2 and δn for edge detection as in (1), but we introduce an extra term based on the available SP to further guide the inversion algorithm in edge detection. The operator LAnMR works as LMn R with only one difference: in addition to the relative magnitude of |∇χn(r)|2 and δn , we have an extra term, Q2|∇P (r)|2, that plays a role in edge reconstruction. We refer to the use of (8) as AMR (Type II).
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