2-D blind deconvolution by partitioning into coupled 1-D problems using discrete Radon transforms

The 2-D blind deconvolution problem is to reconstruct an image (2-D signal) from the 2-D convolution of the image with another, unknown 2-D signal which represents some unknown distortion. The only known information is the result of the convolution and the fact that both 2-D signals have compact support. We solve the 2-D discrete blind deconvolution problem by partitioning it into a mostly-decoupled set of 1-D blind deconvolution problems. We define discrete and modulated Radon transforms to formulate two coupled 1-D problems, the solution to which then specifies solutions to the other decoupled 1-D problems. The latter may in turn be solved in parallel; however, using the solution to one problem as input to a neighboring problem reduces the computation significantly for serial computers. Unlike other exact 2-D blind deconvolution methods which rely on tracking zero curves of algebraic functions or equivalent operations, no continuous-function-based methods are used here. This makes the procedure more robust numerically. By coupling more than two initial problems, the method can be made to work on data with small amounts of noise.