Regularized minimal residual method for permittivity reconstruction in microwave imaging

Abstract

In this paper, a regularized reconstruction based on the minimal residual method is proposed for microwave imaging applications. The method provides optimum regularization parameter to estimate the distribution of permittivity values of unknown scatterers under test. Initially, the method is applied to Born approximated linear model for weak scatterers. The performance of this approach is compared with the commonly adopted Morozov's discrepancy principle used in conjunction with the Tikhonov regularization. The effectiveness of the method is assisted by simulating the various numerical examples of synthetic and experimental data. The results of numerical simulations validate that the proposed method is highly effective. Thereafter, a non‐linear inverse problem based on the inexact Newton method is examined for the estimation of strong scatterers. Here also, the proposed method is found to be helpful in terms of improving the image accuracy.

Distorted Born iterative method with back-propagation improves permittivity reconstruction

“…It decomposes the system matrix as (G Π u i ) = LSR*, where L and R represent the left and right singular matrices, and S denotes the singular value matrix. After simplification, we obtain the contrast function vector as [25]…”

“…It decomposes the system matrix as ( G Π u i ) = LSR *, where L and R represent the left and right singular matrices, and S denotes the singular value matrix. After simplification, we obtain the contrast function vector as [25]where 〈 · , · 〉 represents the inner product, ρ is the rank of the system matrix, σ k denotes the k th singular value, l k is the k th left singular vector, and r k is the k th right singular vector.…”