Angular sampling reduction in SPECT using deep neural networks

Objectives: Scan time and angular sampling number are closely related to the image quality of SPECT acquiring projection data through the periodic rotation of gamma camera. If we can retain image quality with less number of angular samples, we can reduce the scan time for SPECT studies. In this study, we propose deep neural networks that restore fully-sampled sinogram from the half or quarter times angularly under-sampled sinogram.

Methods: Using 769 T1-weighted 3D magnetic resonance images (MRI) segmented into gray matter, white matter and CSF, we generated digital SPECT phantoms representing cerebral perfusion distribution by assigning 1, 0.5 and 0.1 to each region. We performed radon transform with 120 angular samples and added Poisson noise as shown in the supporting materials. Then, we applied Butterworth filter to the projection data (pre-filtering). The filter’s cut-off frequency and degree were 0.6 cyc/cm and 5, respectively. Finally, the sinogram reformatted from the pre-filtered projection data was regarded as ground truth or label, from which we generated under-sampled sinograms. The fully and under-sampled sinograms were reconstructed using filtered back projection (FBP) method utilizing ramp filter. Six hundred and ninety (619) images which consist of 87,751 slices were used to train and test two neural network architectures, convolutional auto-encoder (CAE) and generative adversarial network (GAN). The other 150 images with 21,295 slices were used for testing the networks. The loss function that we minimized to train the CAE was the L1 distance between output and input image, and it is also used as the adversarial loss for GAN. The missing data in under-sampled input was filled with the deep learning output because the input is the true values and our task is to find missing projections. We reconstructed outputs of networks and compared them to reconstructed images of under-sampled sinogram and linearly interpolated sinogram. The peak to signal-to-noise ratio for (PSNR) was calculated to assess the reconstruction results quantitatively.

Results: After training networks with 45 epochs, both CAE and GAN successfully generated real-like sinograms. When the projection data was under-sampled by half, reconstruction results of CAE and GAN showed different behavior. The CAE yielded PSNR (16.30) similar to reconstruction result of under-sampled sinogram (16.37), but the GAN result (15.34) was poorer than the result of linear interpolation (16.19). However, the GAN showed best performance (14.11) for the 1/4 angular projections and the CAE also outperformed the linear interpolation. Conclusion: The results of this study indicate that the proposed deep neural network has great potential as an interpolation method for under-sampled SPECT sinogram, especially at high compression rate. The CAE produces high-quality results for both 1/2 and 1/4 under-sampled data, but we have to be careful about using GAN which creates more realistic samples because this property is stemmed from the randomness of projection data distribution. However, in complex problems such as filling large gaps in sinogram space, the GAN exhibits better performance than CAE because the images to be filled have a greater correlation with themselves.