# A Linear Method for Shape Reconstruction based on the Generalized Multiple Measurement Vectors Model

## TL;DR

This paper introduces a linear shape reconstruction method using the generalized multiple measurement vectors model, leveraging joint sparsity and cross validation to improve accuracy and outperform traditional methods in focusing performance.

## Contribution

It presents a novel linear reconstruction approach based on GMMV, incorporating joint sparsity and CV to enhance shape estimation without noise level prior.

## Key findings

- Outperforms linear sampling method in focusing performance
- Uses cross validation to avoid noise level estimation
- Validates with TM experimental data

## Abstract

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM).