Computing Fourier integral operators with caustics. (25th October 2016) - Caday, Peter
Abstract: Fourier integral operators (FIOs) have widespread applications in imaging, inverse problems, and PDEs. An implementation of a generic algorithm for computing FIOs associated with canonical graphs is presented, based on a recent paper of de Hoop et al . Given the canonical transformation and principal symbol of the operator, a preprocessing step reduces application of an FIO approximately to multiplications, pushforwards and forward and inverse discrete Fourier transforms, which can be computed in O ( N n + ( n − 1 ) / 2 log N ) time for an n -dimensional FIO. The same preprocessed data also allows computation of the inverse and transpose of the FIO, with identical runtime. Examples demonstrate the algorithm's output, and easily extendible MATLAB/C++ source code is available from the author.