Simultaneous Microwave Imaging and Parameter Estimation Using Modified Level-Set Method

A modified level-set method (MLSM) is proposed to simultaneously reconstruct the shape and electrical properties of 2-D objects. As a numerical technique, the formal level-set method (LSM) can retrieve the shape and position of objects, using synthetic/measurement data. In general, the constitutive parameters of an object (e.g., its relative complex permittivity) are among the a priori information needed for the LSM. For MLSM, an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2-D object. The initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized. The cost function is regularized with two penalty terms. To prevent sudden change in the shape of the object, a curvature-based regularization is used. Also, Laplacian regularizer is used to reduce fluctuations in the object's constitutive parameters during the process. Using different synthetic data sets, the capabilities of MLSM in microwave imaging and parameter estimation are evaluated. It is found that, using MLSM, it is possible to completely separate two adjacent objects, separated by a distance of one-fifteenth of a wavelength. The proposed method can retrieve targets of different relative permittivities, with less than 10% error. One interesting feature of this method is its high fidelity in retrieving the immersed one-tenth-wavelength targets in highly contrasting (up to as high as 8:1) domains. In the case of targets with little contrast (10%), the proposed method, with more iterations, can converge on a value, which is 57% more than the actual value. These features are valuable in distinguishing malignant tissue from normal tissue.