Image deconvolution via superfast inversion of a class of two-level Toeplitz matrices

In this work we present an efficient method to recover images that have been corrupted by a certain class of image filters. For this class of filters, the image degradation process is described by a linear system of equations involving a two-level Toeplitz matrix with triangular structure on either the block or subblock level. This type of structure has algebraic properties that allow us to adapt “superfast” methods for Toeplitz matrix inversion to the two-level case. Our novel two-level superfast algorithm performs the majority of its calculation with the Fast Fourier Transform and allows us to invert an N × N matrix in O(N log N) with reasonable overhead constant. To demonstrate the power of the algorithm we deblur severely corrupted images in short execution times.