ET Bayesian reconstruction using automatic bandwidth selection for joint entropy optimization

Abstract

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.

Information theoretic regularization in diffuse optical tomography

“…Parts of this work have also contributed to publications in other modalities (PET/SPECT) [Kazantsev et al, 2010;Pedemonte et al, 2010a;Somayajula et al, 2010] as well as one undergoing completion [Pedemonte et al, 2010b]. We aim to publish the SRR scheme for DOT in the near future.…”

“…Class conditional entropic prior for MRI enhanced SPECT reconstruction. In proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference, • Kazantsev, D., Pedemonte, S., Bousse, A., Panagiotou, C., Arridge, S., Hutton, B. F., and Ourselin, S. (2010).…”

“…For a detailed introduction on kernel width selection methods, the reader is is redirected to specialized literature and the references within [Hall et al, 1991;Hansen, 1992aHansen, , 1998Jones et al, 1996;Raykar and Duraiswami, 2006;Silverman and Green, 1986;Turlach, 1993;Vogel, 2002]. In addition, many optimization problems which involve a KDE incorporate the bandwidth of the kernel in the overall set of optimized parameters -see for example [Kazantsev et al, 2010;Viola, 1995].…”

“…In this work we do not optimize for u. The reader is directed to our recent work of applying information theoretic regularization in positron emission tomography (PET) simultaneously with a search for u [Kazantsev et al, 2010].…”

“…In addition, it has been used for information theoretic regularization of positron emission tomography (PET) using structural priors [Kazantsev et al, 2010;Pedemonte et al, 2010a;Somayajula et al, 2010] as well as Pedemonte et al [2010b] which is work-in-progress.…”