A Novel Microwave Imaging Approach Based on Regularization in $L^{p}$ Banach Spaces

Electromagnetic Inverse-Scattering Reconstructions by an Inexact Newton Method: Numerical and Experimental Results

“…Results can be found in the mentioned references. Concerning in particular the improvement related to the new version developed in the p L Banach space, it has been shown [54] that, for p = 1.2, we can expect a reduction of the mean reconstruction error on the contrast function inside the investigation domain of about 30% when compared with the same solution obtained in the Hilbert space (for a homogeneous cylinder with a triangular cross section of side 0.5λ, λ being the wavelength of the incident radiation, c = 1-j0.3, 8 line-current sources, 241 measurement points, and a signal to noise (SNR) ratio on the simulated scattered field of 20 dB). More relevant, the improvement becomes more and more evident when the noise on the data increases.…”

“…Recently, a different approach has been proposed [54]. In particular, a different cost functional is assumed, i.e., L norm.…”

“…This choice gives rise to a substantial reduction of the over-smoothing in the restored solution and has been proven to provide more accurate reconstructions. However, the INM required significant modifications, which are detailed in [54]. In particular, the inner loop is based on the following recursive relation ( 0 …”

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

“…Recently, they have been developed also with reference to Lp Banach spaces [112,113], where the oversmoothing effects usually associated with regularization procedures developed in the common Hilbert space seem to be mitigated. It should be also noticed that sparsity concepts and compressive sensing can be successfully adopted [114,115].…”

Swarm Optimization Methods in Microwave Imaging

“…This is often a common choice in microwave imaging and allows the use of widely studied mathematical tools for the analysis of the convergence and regularization behaviors. However, different norms have been recently proposed, too (e.g., the norm of L p Banach spaces [42]). For illustrative purposes, the case of cylindrical dielectric targets embedded in free space is explicitly described in the following.…”