Obtaining accurate and reliable images from low-dose computed tomography (CT) is challenging. Regression convolutional neural network (CNN) models that are learned from training data are increasingly gaining attention in low-dose CT reconstruction. This paper modifies the architecture of an iterative regression CNN, BCD-Net, for fast, stable, and accurate low-dose CT reconstruction, and presents the convergence property of the modified BCD-Net. Numerical results with phantom data show that applying faster numerical solvers to model-based image reconstruction (MBIR) modules of BCD-Net leads to faster and more accurate BCD-Net; BCD-Net significantly improves the reconstruction accuracy, compared to the state-of-the-art MBIR method using learned transforms; BCD-Net achieves better image quality, compared to a state-of-the-art iterative NN architecture, ADMM-Net. Numerical results with clinical data show that BCD-Net generalizes significantly better than a state-of-the-art deep (non-iterative) regression NN, FBPConvNet, that lacks MBIR modules.

Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image reconstruction (MBIR), using more iterations of an unregularized method may increase the noise, so incorporating regularization into the image reconstruction is desirable to control the noise. New regularization methods based on learned convolutional operators are emerging in MBIR. We modify the architecture of a variational neural network, BCD-Net, for PET MBIR, and demonstrate the efficacy of the trained BCD-Net using XCAT phantom data that simulates the low true coincidence count-rates with high random fractions typical for Y-90 PET patient imaging after Y-90 microsphere radioembolization. Numerical results show that the proposed BCD-Net significantly improves PET reconstruction performance compared to MBIR methods using non-trained regularizers, total variation (TV) and non-local means (NLM), and a non-MBIR method using a single forward pass deep neural network, U-Net. BCD-Net improved activity recovery for a hot sphere significantly and reduced noise, whereas non-trained regularizers had a trade-off between noise and quantification. BCD-Net improved CNR and RMSE by 43.4% (85.7%) and 12.9% (29.1%) compared to TV (NLM) regularized MBIR. Moreover, whereas the image reconstruction results show that the non-MBIR U-Net over-fits the training data, BCD-Net successfully generalizes to data that differs from training data. Improvements were also demonstrated for the clinically relevant phantom measurement data where we used training and testing datasets having very different activity distribution and count-level.

Using learned convolutional operators for iterative signal/image recovery is a growing trend in computational imaging [1]-[6] due to its outperforming signal recovery performances over conventional non-trained regularizers (e.g., sparsity promoting regularizers) [4]-[6]. The iterative image recovery approaches using a learned convolutional operator or convolutional neural network (CNN) closely relate to challenging (nonconvex) block optimization. The authors in [4]-[6] proposed a fast and convergence-guaranteed block proximal gradient method using a majorizer to quickly and stably recover images with the aforementioned image recovery approaches. Nonetheless, the corresponding iterative algorithm needs several hundreds of iterations to converge, detracting from its practical use. By unfolding iterative signal recovery algorithms, there exist several works in combining neural network approaches into them [7]-[14]. By optimizing image mapping networks-- consisting of encoding and decoding kernels, thresholding operators, etc.--at each iteration (or layer), the methods moderate the aforementioned convergence issue, aiming to give "best" signal estimates at each layer.