Partial Volume Correction using Median Priors in Penalized-Likelihood Image Reconstruction Methods

Partial volume error (PVE) is an important problem in quantitative image reconstruction. PVE is induced due to the low resolution capabilities of the imaging system. Additionally, reconstructed images have non-uniform resolution across the field of view. This non-uniform resolution is a consequence of a number of physical and detector dependent effects, such as non-uniform object attenuation, scatter or crystal penetration effect. A specific problem being addressed is that of the variation of PVE resulting from spatial variations in reconstructed resolution. Regularization is preferably used to overcome variations in underlying signal and noise. The penalized-likelihood (PL) image reconstruction methods use some kind of penalty function to regularize the image and they impose certain conditions to obtain reconstructed images with acceptable signal to noise ratio. Among different penalty functions, median priors have reasonable smoothing and edge preserving properties. Though non-quadratic priors can be used for edge preservation, they require several parameters to be tuned. We have used quadratic (QP) and median priors (MP) to achieve better control of resolution characteristics and partial volume correction. The Geometric Transfer Matrix (GTM) method is one of the methods which try to extract mean activities in various regions of the object using geometric transfer coefficients through an application of partial volume correction at the same time. We implemented the GTM method with PL methods using MPs and compared the results with QPs.