Bayesian image analysis in Fourier space

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Project Summary/Abstract: “Bayesian image analysis in Fourier space (BIFS)” The objective of this grant is to develop a family of new medical imaging processing methods that will advance the state-of-the art in radiological research and diagnostic evaluation. We will improve on commonly used spatial filtering methods, Fourier/wavelet shrinkage/sparsity methods, and conventional Bayesian image analysis methods by reformulating Bayesian Image analysis in Fourier Space (BIFS), i.e., by modeling in terms of spatial frequencies. Spatially correlated prior distributions that are difficult to model and compute in conventional image space can be more efficiently modeled as a set of independent processes across Fourier space. The originally inter-correlated and high-dimensional problem in image space is thereby broken down into a series of independent one-dimensional problems in Fourier space, where the independent distributions are tied together by our development of a parameter function over Fourier space. This independence over Fourier space structure coupled with the concept of the parameter function will enable us to develop new families of powerful and easy to specify BIFS models with fast algorithms to compute posterior image estimates. We will disseminate these methods to imaging researchers and clinical practitioners by developing a BIFS software package designed to solve a wide range of medical image processing problems. The specific aims of the proposal are: 1) to develop novel BIFS models targeted to provide improved solutions to medical image processing problems; 2) to validate benefits of BIFS models compared with conventional processing methods based on careful simulation and phantom imaging studies; 3) to clinically validate improvements generated by BIFS modeling in two ongoing clinical studies: a) quantification of brain perfusion patterns associated with frontotemporal lobar dementia, and b) detection of breast cancer in MRIs; and 4) to disseminate the methods to the wider clinical and scientific communities by generating and releasing an R package for the implementation of BIFS. Our innovative BIFS modeling approach has the potential to make a big difference in the field of medical image processing problems and image analysis in general. The impact on radiological application through the development of new, readily implementable and fast-to-compute BIFS models will lead to increased accuracy for the detection of findings in radiological screening and diagnosis; improved assessment of treatment efficacy; increased accuracy for measuring disease effects in imaging-based clinical studies; and expanded potential for practical image data-mining.