Direct Sampling Method for Diffusive Optical Tomography

In this work, we are concerned with the di↵usive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and e cient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its e↵ectiveness and robustness against noise in the data. This provides a new promising numerical strategy for the DOT problem. Mathematics Subject Classification (MSC2000): 35J67, 35R30, 65N21, 78A70, 78M25.