Penalized PET Reconstruction Using Deep Learning Prior and Local Linear Fitting

Abstract

Motivated by the great potential of deep learning in medical imaging, we propose an iterative positron emission tomography reconstruction framework using a deep learning-based prior. We utilized the denoising convolutional neural network (DnCNN) method and trained the network using full-dose images as the ground truth and low dose images reconstructed from downsampled data by Poisson thinning as input. Since most published deep networks are trained at a predetermined noise level, the noise level disparity of training and testing data is a major problem for their applicability as a generalized prior. In particular, the noise level significantly changes in each iteration, which can potentially degrade the overall performance of iterative reconstruction. Due to insufficient existing studies, we conducted simulations and evaluated the degradation of performance at various noise conditions. Our findings indicated that DnCNN produces additional bias induced by the disparity of noise levels. To address this issue, we propose a local linear fitting function incorporated with the DnCNN prior to improve the image quality by preventing unwanted bias. We demonstrate that the resultant method is robust against noise level disparities despite the network being trained at a predetermined noise level. By means of bias and standard deviation studies via both simulations and clinical experiments, we show that the proposed method outperforms conventional methods based on total variation and non-local means penalties. We thereby confirm that the proposed method improves the reconstruction result both quantitatively and qualitatively.

Fig. 1.

(a) Training of DnCNN with full dose image as the groud truth and low dose image as input. Low dose data is generated by Poisson thining process at a pre-defined noise level ϵ, and multislices along axial direction are used. (b) The trained DnCNN and local linear fitting are combined in iterative PET reconstruction.

Fig. 2.

(a) The performance of noise reduction for different downsampling datasets. Because we trained the network using 6× downsampled data, the performace was highest with the 6× downsampled data. (b) Comparison of bias increase by iteration. We iterated DnCNN and DnCNN with LLF by setting the output image as input of next iteration. (c) Comparison of bias and standard deviation.

Fig. 3.

Reconstructed images using EM and DnCNN (a) without LLF and (b) with LLF at iterations (i) 2, (ii) 5 and (iii) 8.

Fig. 4.

Bias and standard deviation studies for OPOSEM image with Gaussian filtering, OS-SQS with TV, OS-SQS with NLM, OS-SQS with DnCNN and the proposed method, calculated from 20 random datasets with 10× downsampling factor. By selecting similar biases, the hyper-parameters of (i) were used for image quality comparison throughout our experiments. The OPOSEM image using full data was used as the ground truth.

Fig. 5.

Image comparison of (a) full dose OPOSEM image, (b) 10× low dose OPOSEM image, (c) 10× low dose OPOSEM image with Gaussian filtering of FWHM 2.4 mm and (d) 10× low dose OPOSEM image with DnCNN. Iterative reconstrution images using (e) OS-SQS with TV, (f) OS-SQS with NLM and (g) the proposed method. The initial image of (e)–(g) is 10× low dose OPOSEM image. Magnified views of (i) full dose OPOSEM image, (ii) OS-SQS with NLM and (iii) the proposed method; and ROI in (i) is used for SSIM comparison.

Fig. 6.

Convergence study using various downsampling factors: (a) 4, (b) 6, (c) 8 and (d) 10. The initial image was OPOSEM image using each downsampled data. The converged images were compared at 100 iterations.

Fig. 7.

Coronal views of reconstructed images using DnCNNs trained with (a) single slice and (b) five slices.

Fig. 8.

Comparison of NRMSEs using the guided filter and the LLF.