###### Abstract  
Recently, an extended family of power-divergence measures with two parameters was proposed together with an iterative reconstruction algorithm based on minimization of the divergence measure as an objective function of the reconstructed images for computed tomography. Numerical experiments on the reconstruction algorithm illustrated that it has advantages over conventional iterative methods from noisy measured projections by setting appropriate values of the parameters. In this paper, we present a novel neural network architecture for determining the most appropriate parameters depending on the noise level of the projections and the shape of the target image. Through experiments, we show that the algorithm of the architecture, which has an optimization sub-network with multiplicative connections rather than additive ones, works well.  
deep learning: computed tomography; iterative image reconstruction; learned optimization algorithm +
Footnote †: journal:  
0000-0001-6000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-00000-00000-0000  
of projection noise. As a natural conjecture, the appropriate parameters also depend on the shape of the image to be reconstructed, so one may consider whether it is possible to develop a method for estimating the parameters from the measured projection.  
In recent years, many studies have incorporated deep-learning approaches for parameter estimation in iterative algorithms [29; 30; 31; 32; 33; 34; 35]. The well-known methods of ADMM-Net [32] and ISTA-Net [34] embed an iterative algorithm into a deep neural network by using the alternating direction method of multipliers [36] and the iterative shrinkage thresholding algorithm [37], respectively. Some of these studies have used recurrent neural networks (RNNs) in which convolutional sub-networks for estimating parameters are used in each iterative calculation and the iterative calculations are intertwined [29; 33]. The complexity of the networks increases in proportion to the number of iterative calculations, but the risk of the vanishing gradient problem [38] occurring is low because the calculations are implemented as residual blocks [39]. The ideas behind this neural network architecture (referred to below as learned optimization; LO) have been organized by [PERSON] et al. [40], and LO has been actively improved in terms of its design, training method, performance, and operation [41; 42; 43; 44; 45; 46; 47]. In particular, this technique has been applied to the field of medical imaging, especially the problem of compressed sensing in magnetic resonance imaging [48; 49; 50]. [PERSON] et al. [51] used it together with [PERSON]'s acceleration [52] to estimate parameters associated with the regularization term for compensating for a lack of signals.  
In this paper, we propose a novel neural-network architecture that estimates the values of parameters in the PDEM algorithm by using projection data. The proposed architecture is similar to LO because it has two subsystems for estimating parameters and iterative operations. Following the naming convention of [PERSON] et al., we call these subsystems the optimizer and optimizee, respectively. Unlike conventional LO, the subsystems are completely separated in our system, and the network architecture is more straightforward than that of RNNs. The traditional LO estimates parameters by using the results of each iterative calculation, whereas our architecture uses only projection data. Nevertheless, the experimental results illustrate that our method works well. Moreover, the optimizee has a different structure than the traditional optimizee, with multiplicative rather than additive connections.