LOCALLY WEIGHTED TOTAL VARIATION DENOISING FOR PSF MODELING ARTIFACT SUPPRESSION IN PET RECONSTRUCTION Arthur Mikhno 1 , Elsa D. Angelini 1, 2 , and Andrew F. Laine 1 1. Department of Biomedical Engineering, Columbia University, New York 2. Institut Mines-Telecom, Telecom ParisTech, CNRS LTCI, Paris, France ABSTRACT Incorporating the point spread function (PSF) into the itera- tive MLEM reconstruction of PET images introduces contrast and size dependent ringing and over enhancement artifacts. We previously developed a new method, called TV-PSF- MLEM, to suppress these artifacts based on the introduction of a locally-weighted total variation regularization within the MLEM reconstruction algorithm. On non-noisy PET mea- sures, we proposed to compute the TV spatial weights based on the point-wise convergence rate of a preliminary MLEM reconstruction, for each voxel. In this work we extend the TV- PSF-MLEM weighting scheme to noisy measures introducing a noise-independent weighting scheme. We compare its per- formance to a state of the art PET denoising method. Results on numerical phantoms show that the TV-PSF-MLEM offers substantial advantages in the recovery of small cylinders and gains in contrast recovery of larger cylinders. Index Terms— PET, image reconstruction, point spread function, MLEM, Total Variation 1. INTRODUCTION Iterative reconstruction techniques, such as the maximum likelihood expectation maximization (MLEM), provide a flexible framework in positron emission tomography (PET) imaging for modeling the physics and the scanner geome- try, yielding greater image contrast, visual quality and noise robustness than analytical reconstruction methods. Incorpo- rating the point spread function (PSF) of the scanner into the iterative MLEM reconstruction process (called PSF-MLEM) improves spatial resolution but introduces significant contrast and size dependent over-enhancement and ringing artifacts [1, 2]. The over-enhancement artifacts might be explained by the mismatch between the true and the measured PSF, while the ringing artifacts are related to object sizes [3]. Most ap- proaches previously proposed to compensate ringing artifacts tend to blur the PET data which undermines the benefits of including the PSF in the reconstruction [3]. A promising approach was recently proposed by Rapis- arda et al. for artifact suppression by incorporating a new reg- ularization prior into the reconstruction process that locally modifies the image estimate at each iteration in an attempt to locally control edge enhancement [4]. This method pro- vides excellent ringing suppression in the image, especially for large structures, but also tends to suppress the benefits of PSF modeling in smaller objects. We previously developed a new method (called TV-PSF- MLEM) to suppress PSF-MLEM artifacts based on a locally weighted total variation regularization applied at each itera- tion [5]. Amplitude of the weights specify the amount of TV regularization at each voxel. These local weights can be pre- calculated based on the convergence rate of MLEM at each voxel since we established that the convergence rate is di- rectly related to the object size and contrast and that artifact magnitudes are directly proportional to this convergence rate. Using noiseless simulations, we showed that TV-PSF-MLEM suppress ringing artifact while providing edge and contrast recovery, beyond that of standard MLEM, especially in small cylinders. In this paper we extend the TV-PSF-MLEM for- malism to simulations corrupted with Poisson noise. A new weighting scheme is introduced robust to noise and results are presented, comparing to the Rapisarda method that is also based on a regularization prior. 2. METHODOLOGY 2.1. Iterative image reconstruction: MLEM algorithm The ML estimate of the PET image is computed using the MLEM algorithm, and following the notation from [4], leads to the following iterative update equation: λ k+1 b = λ k b BP b 1 BP b y d P d λ k b 0 = λ k b u k b (1) where λ k b represents the intensity of the voxel b within the im- age λ at iteration k, y d is the sinogram measure, equal to the number of counts along the line of response (LOR) d, and 1 is a unit matrix of the same size as y d . Following the method- ology introduced in [4], incorporating the PSF model into Eq. (1) is achieved by modifying the projector P and backprojec- tor BP as follows: P d (·) b = X ((·) * PSF ) b p bd BP b (·) d = PSF T X (·) d p bd (2) 971 U.S. Government work not protected by U.S. copyright