Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor

A reconstruction algorithm to simultaneously estimate the shape and location of three-dimensional breast cancer tumor is presented and its utility is analyzed. The approach is based on a spherical harmonic decomposition to capture the shape of the tumor. We combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor. The results demonstrate the potential advantage of collecting data using a multiple-view/tomographic-type strategy. We show how the order of the harmonic expansion must be increased to capture increasingly "irregularly" shaped tumors and explore the resulting increase in the central processing unit (CPU) time required by the algorithm. Our approach shows accurate reconstruction of the tumor image regardless of the source polarization. This work demonstrates the promise of the algorithm when used on data corrupted with Gaussian noise and when perfect knowledge of the tumor electrical properties is not available.