Abstract
In PET image reconstruction, regularization is often needed to reduce the noise in the resulting images. Patch-based image processing techniques have recently been successfully used for regularization in medical image reconstruction through a penalized likelihood framework. Re-parameterization within reconstruction is another powerful regularization technique in which the object in the scanner is re-parameterized using coefficients for spatially-extensive basis vectors. In this work, a method for extracting patch-based basis vectors from the subject’s MR image is proposed. The coefficients for these basis vectors are then estimated using the conventional MLEM algorithm. Furthermore, using the alternating direction method of multipliers, an algorithm for optimizing the Poisson log-likelihood while imposing sparsity on the parameters is also proposed. This novel method is then utilized to find sparse coefficients for the patch-based basis vectors extracted from the MR image. The results indicate the superiority of the proposed methods to patch-based regularization using the penalized likelihood framework.
Highlights
PET image reconstruction seeks to estimate a 3D image of the radiotracer concentration from line of response measurements
Sparse C-PB-alternate direction method of multipliers (ADMM) gives a slightly lower best mean pixel-based normalized root mean squared error (n-RMSE) value within the brain at the best iteration number compared to C-PB-maximum likelihood expectation maximization (MLEM), while the opposite is the case for mean contrast recovery coefficient (CRC) of the hot lesion in white matter
A novel re-parameterization framework which uses patch-based basis functions learned from a registered prior image for PET image reconstruction is devised
Summary
PET image reconstruction seeks to estimate a 3D image (i.e. object representation) of the radiotracer concentration from line of response measurements. The literature on regularization in PET reconstruction can be divided into two main categories: (i) including a prior function in the objective using a maximum a posteriori (MAP) framework and (ii) representing the radioactive distribution as a superposition of spatial basis vectors such as blobs (re-parameterization). The authors in Chen et al (2015) and Tang et al (2014) have proposed PET image reconstruction methods that use sparse representation of image patches using a dictionary learned from anatomical images These methods are based on a Bayesian (or MAP) framework where the regularized objective function is composed of a data fidelity term and a sparse representation error term. In order to enhance readability, throughout the paper, bold capital letters are used to indicate matrices, bold lower-case letters represent column vectors and all non-bold letters denote scalar values
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