Post-reconstruction deconvolution of PET images by total generalized variation regularization

Abstract

Improving the quality of positron emission tomography (PET) images, affected by low resolution and high level of noise, is a challenging task in nuclear medicine and radiotherapy. This work proposes a restoration method, achieved after tomographic reconstruction of the images and targeting clinical situations where raw data are often not accessible. Based on inverse problem methods, our contribution introduces the recently developed total generalized variation (TGV) norm to regularize PET image deconvolution. Moreover, we stabilize this procedure with additional image constraints such as positivity and photometry invariance. A criterion for updating and adjusting automatically the regularization parameter in case of Poisson noise is also presented. Experiments are conducted on both synthetic data and real patient images.

Relaxed ordered subset preconditioned alternating projection algorithm for PET reconstruction with automated penalty weight selection

“…Several researchers have shown that the DP can be used to guide penalty weight selection. In particular, Guerit et al have shown via KL‐divergence that a penalty sub‐update can be added to Poisson denoising algorithms. However, this method relies on the Poisson discrepancy metric for image quality, which may not be optimal in the MMSE sense, and its extension to a two parameter model is unclear.…”

“…At present, several researchers have developed theoretical frameworks based on the discrepancy principle (DP) given Gaussian and Poisson noise for estimating the penalty weights of single parameters. [28][29][30][31] The DP is the idea that the uncertainty of the data should match the variability of the object or penalty function. However, it has been pointed out by several researchers that this match does not necessarily result in a minimum mean squared error (MMSE) image, 32,33 nor if MMSE is necessarily the right goal.…”

“…), data from that class member, and a particular image quality metric, there were no simple theoretical means with which to choose the optimal penalty weights. At present, several researchers have developed theoretical frameworks based on the discrepancy principle (DP) given Gaussian and Poisson noise for estimating the penalty weights of single parameters …”

Compressive lensless endoscopy with partial speckle scanning

“…Since the synthetic USAF transmission target is piecewise constant, we select the TV-norm for g 1 in Eqs. (30) and (37).…”

Spatio-spectral deconvolution of vector valued images using total nuclear variation

“…This setting is of interest whenever one has no direct access to the sinogram of the acquisition. We also note that a second-order deconvolution approach, based on total generalized variation [8] has been proposed for static PET images in [9].…”