  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.
