Image reconstruction without prior information

Abstract

A novel framework for designing image reconstruction algorithms for linear forward problems is proposed. The framework is based on the novel concept of conserving the information in the data during image reconstruction rather than supplementing it with prior information. The framework offers an explanation as to why the popular reconstruction algorithms for MRI, CT and convolution are generally expressible as left invertible matrices. Also, the framework can be used to improve linear deconvolution and tackle such stubborn linear inverse problems as the Laplace transform.