ET Bayesian reconstruction using automatic bandwidth selection for joint entropy optimization

In emission tomography (ET), fast developing Bayesian reconstruction methods can incorporate anatomical information derived from co-registered scanning modalities, such as magnetic resonance (MR) and computed tomography (CT). We propose a Bayesian image reconstruction method for single photon emission computed tomography (SPECT), using a joint entropy (JE) similarity measure to embed MR anatomical data. An optimized non-parametric Parzen window approach is used for fast and efficient estimation of the probability density function (PDF) of the JE metric. It is known that the quality of the Parzen estimates strongly depends on the kernel bandwidth of the smoothing function. When the density is over or under-smoothed, because of too large or small bandwidth value, this leads to an incorrect entropy estimate and, eventually, to a biased solution. To alleviate the problem of searching manually for the most suitable weight for the smoothing function and the number of bins for the histogram, we use an adaptive method to find these parameters automatically from the data on each iteration of the Bayesian algorithm. We assess the NRMSE-variance behaviour of the MAP-EM reconstruction method in relation to the quality of the PDF building. For the different bandwidth values of the Gaussian kernel for the density function, an emission image is reconstructed using MR data as a prior. Preliminary numerical experiments are performed using simulated co-registered 2D and 3D SPECT/MR data. Comparison of proposed technique with neighbourhood dependent anatomically-based prior is presented. Lesions are simulated to be apparent on the gray matter of the 3D SPECT data, but invisible on MRI. Preliminary results demonstrate that applying optimal density estimation for JE metric is feasible and more efficient compared to non-adaptive techniques