Analytical reconstruction of deconvolved Fourier rebinned PET sinograms

Direct mapping from PET coincidence data to proton-dose and positron activity using a deep learning approach

Objective. Obtaining the intrinsic dose distributions in particle therapy is a challenging problem that needs to be addressed by imaging algorithms to take advantage of secondary particle detectors. In this work, we investigate the utility of deep learning methods for achieving direct mapping from detector data to the intrinsic dose distribution. Approach. We performed Monte Carlo simulations using GATE/Geant4 10.4 simulation toolkits to generate a dataset using human CT phantom irradiated with high-energy protons and imaged with compact in-beam PET for realistic beam delivery in a single-fraction (∼2 Gy). We developed a neural network model based on conditional generative adversarial networks to generate dose maps conditioned on coincidence distributions in the detector. The model performance is evaluated by the mean relative error, absolute dose fraction difference, and shift in Bragg peak position. Main results. The relative deviation in the dose and range of the distributions predicted by the model from the true values for mono-energetic irradiation between 50 and 122 MeV lie within 1% and 2%, respectively. This was achieved using 105 coincidences acquired five minutes after irradiation. The relative deviation in the dose and range for spread-out Bragg peak distributions were within 1% and 2.6% uncertainties, respectively. Significance. An important aspect of this study is the demonstration of a method for direct mapping from detector counts to dose domain using the low count data of compact detectors suited for practical implementation in particle therapy. Including additional prior information in the future can further expand the scope of our model and also extend its application to other areas of medical imaging.

Iterative reconstruction of Fourier-rebinned PET data using sinogram blurring function estimated from point source scans

PURPOSE

The accuracy of the system model that governs the transformation from the image space to the projection space in positron emission tomography (PET) greatly affects the quality of reconstructed images. For efficient computation in iterative reconstructions, the system model in PET can be factored into a product of geometric projection and sinogram blurring function. To further speed up reconstruction, fully 3D PET data can be rebinned into a stack of 2D sinograms and then be reconstructed using 2D iterative algorithms. The purpose of this work is to develop a method to estimate the sinogram blurring function to be used in reconstruction of Fourier-rebinned data.

METHODS

In a previous work, the authors developed an approach to estimating the sinogram blurring function of nonrebinned PET data from experimental scans of point sources. In this study, the authors extend this method to the estimation of sinogram blurring function for Fourier-rebinned PET data. A point source was scanned at a set of sampled positions in the microPET II scanner. The sinogram blurring function is considered to be separable between the transaxial and axial directions. A radially and angularly variant 2D blurring function is estimated from Fourier-rebinned point source scans to model the transaxial blurring with consideration of the detector block structure of the scanner; a space-variant 1D blurring kernel along the axial direction is estimated separately to model the correlation between neighboring planes due to detector intrinsic blurring and Fourier rebinning. The estimated sinogram blurring function is incorporated in a 2D maximum a posteriori (MAP) reconstruction algorithm for image reconstruction.

RESULTS

Physical phantom experiments were performed on the microPET II scanner to validate the proposed method. The authors compared the proposed method to 2D MAP reconstruction without sinogram blurring model and 2D MAP reconstruction with a Monte Carlo based blurring model. The results show that the proposed method produces images with improved contrast and spatial resolution. The reconstruction time is unaffected by the new method since the blurring component takes a relatively negligible part of the overall reconstruction time.

CONCLUSIONS

The proposed method can estimate sinogram blurring matrix for Fourier-rebinned PET data and can be used to improve contrast and spatial resolution of reconstructed images. The method can be applied to other human and animal scanners.

Partial volume effect correction in PET using regularized iterative deconvolution with variance control based on local topology

Correcting positron emission tomography (PET) images for the partial volume effect (PVE) due to the limited resolution of PET has been a long-standing challenge. Various approaches including incorporation of the system response function in the reconstruction have been previously tested. We present a post-reconstruction PVE correction based on iterative deconvolution using a 3D maximum likelihood expectation-maximization (MLEM) algorithm. To achieve convergence we used a one step late (OSL) regularization procedure based on the assumption of local monotonic behavior of the PET signal following Alenius et al. This technique was further modified to selectively control variance depending on the local topology of the PET image. No prior 'anatomic' information is needed in this approach. An estimate of the noise properties of the image is used instead. The procedure was tested for symmetric and isotropic deconvolution functions with Gaussian shape and full width at half-maximum (FWHM) ranging from 6.31 mm to infinity. The method was applied to simulated and experimental scans of the NEMA NU 2 image quality phantom with the GE Discovery LS PET/CT scanner. The phantom contained uniform activity spheres with diameters ranging from 1 cm to 3.7 cm within uniform background. The optimal sphere activity to variance ratio was obtained when the deconvolution function was replaced by a step function few voxels wide. In this case, the deconvolution method converged in approximately 3-5 iterations for most points on both the simulated and experimental images. For the 1 cm diameter sphere, the contrast recovery improved from 12% to 36% in the simulated and from 21% to 55% in the experimental data. Recovery coefficients between 80% and 120% were obtained for all larger spheres, except for the 13 mm diameter sphere in the simulated scan (68%). No increase in variance was observed except for a few voxels neighboring strong activity gradients and inside the largest spheres. Testing the method for patient images increased the visibility of small lesions in non-uniform background and preserved the overall image quality. Regularized iterative deconvolution with variance control based on the local properties of the PET image and on estimated image noise is a promising approach for partial volume effect corrections in PET.

Statistical image reconstruction from correlated data with applications to PET

Most statistical reconstruction methods for emission tomography are designed for data modeled as conditionally independent Poisson variates. In reality, due to scanner detectors, electronics and data processing, correlations are introduced into the data resulting in dependent variates. In general, these correlations are ignored because they are difficult to measure and lead to computationally challenging statistical reconstruction algorithms. This work addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. In general, correlated variates have a large non-diagonal covariance matrix that is computationally challenging to use as a weighting term in a reconstruction algorithm. This work proposes two methods to simplify the use of a non-diagonal covariance matrix as the weighting term by (a) limiting the number of dimensions in which the correlations are modeled and (b) adopting flexible, yet computationally tractable, models for correlation structure. We apply and test these methods with simple simulated PET data and data processed with the Fourier rebinning algorithm which include the one-dimensional correlations in the axial direction and the two-dimensional correlations in the transaxial directions. The methods are incorporated into a penalized weighted least-squares 2D reconstruction and compared with a conventional maximum a posteriori approach.