3-D Level Set Method for Joint Contrast and Shape Recovery in Microwave Imaging

We propose a three-dimensional (3-D) fast level set method, which can estimate both object shape and dielectric contrast with reduced computational cost. In prior work, we presented a 2-D fast level set method that integrated the level set inversion within the Born iterative method (BIM). This approach significantly reduced the computational cost; however, it was limited to estimating object shape without providing any dielectric contrast inversion. In this paper, we extend our previous method to 3-D and add the capability to estimate dielectric contrast in addition to the shape. The contrast estimation is formulated as a separate step within the BIM iteration, such that the shape and contrast are estimated sequentially in each BIM iteration. This modular framework enables the freedom to choose any arbitrary constraints on the contrast in the cost function. Here, we demonstrate the applicability of a total-variation constraint for the contrast cost function. To validate the method, synthetic data are generated for objects within a 3-D imaging cavity and are then used to test for robustness against variations in object shape, size, position, and contrast. Further, the method is tested on MRI-derived numerical breast phantoms. The reconstructed images indicate that the method can produce accurate estimates of object location, shape, and size while recovering the contrast with an error lower than $\text{2}\%$.