Bayesian Blind Separation and Deconvolution 

A common problem of imaging 3-D objects into image plane is superposition of the projected structures. In dynamic imaging, projection overlaps of organs and tissues complicate extraction of signals specific to individual structures with different dynamics. The problem manifests itself also in dynamic tomography as tissue mixtures are present in voxels. Separation of signals specific to dynamic structures belongs to the category of blind source separation. It is an underdetermined problem with many possible solutions. Existing separation methods select the solution that best matches their additional assumptions on the source model. We propose a novel blind source separation method based on probabilistic model of dynamic image sequences assuming each source dynamics as convolution of an input function and a source specific kernel (modeling organ impulse response or retention function).

These assumptions are formalized as a Bayesian model with hierarchical prior and solved by the Variational Bayes method. The proposed prior distribution assigns higher probability to sparse source images and sparse convolution kernels. We show that the results of separation are relevant to selected tasks of dynamic renal scintigraphy. Accuracy of tissue separation with simulated and clinical data provided by the proposed method outperformed accuracy of previously developed methods measured by the mean square and mean absolute errors of estimation of simulated sources and the sources separated by an expert physician. MATLAB implementation of the algorithm is available for download.