Information, language, and pixon-based image reconstruction
Richard C. Puetter · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
From an information theoretic point of view, the inverse problem and the problem of data compression are intimately related. Optimal compression seeks the most concise representation of a data set, while Bayesian probability theory favors image reconstruction algorithms which minimally model the information present in the data. This should not be surprising. It is in keeping with a scientist's intuitive need to satisfy the precepts of Occam's Razor, i.e. not to over interpret one's data. Information scientists might describe this process as quantifying the algorithmic information content (AIC) of the image, and then using this 'coordinate system' for optimal image reconstruction. The present paper describes pixon- based image reconstruction, a technique based upon AIC minimal image models. Because AIC is language dependent (description length and language complexity are inversely related) we have based the practical implementation of our method on concise (descriptive) languages for generic images, e.g. multiresolution basis functions. The present paper describes both the theory of pixon-based reconstruction and presents practical examples demonstrating that pixon-based reconstruction produces results consistently superior (often by large factors) to those of other methods, including the best examples of maximum likelihood and maximum entropy image reconstruction.