# CTprintNet: An Accurate and Stable Deep Unfolding Approach for Few-View CT Reconstruction
###### Abstract  
In this paper, we propose a new deep learning approach based on unfolded neural networks for the reconstruction of X-ray computed tomography images from few views. We start from a model-based approach in a compressed sensing framework, described by the minimization of a least squares function plus an edge-preserving prior on the solution. In particular, the proposed network automatically estimates the internal parameters of a proximal interior point method for the solution of the optimization problem. The numerical tests performed on both a synthetic and a real dataset show the effectiveness of the framework in terms of accuracy and robustness with respect to noise on the input sinogram when compared to other different data-driven approaches. few-view computed tomography; unfolded neural networks; proximal interior point +
Footnote †: journal:  
00 000-0001-6600-0001-6600][PERSON]  
0000-0001-6600-0001-6600-0001-6600-0001-6600-0001-6600-0001-6600-0001-66000-0001-66000-001-66000-0001-66000-0001-66000-0001-66000-0001-6  
In the last decade, motivated by the availability of huge datasets and new efficient computational devices, such as dedicated graphics processing units (GPUs), deep neural networks (DNNs), in particular convolutional neural networks (CNNs), have been successfully employed for X-ray CT image reconstruction, producing very accurate reconstructions at the expense of explainability and robustness to noise. Deep-learning-based methods used for CT can be grouped into four classes. The first class is called _data-to-image_, and here, the neural network directly maps the acquired sinogram to the reconstructed image (see, for example, [9]). This approach is not widely used since it is well known that it is not stable with respect to noise in the data [10]. The second class is composed of networks directly mapping coarse reconstructed images to accurate reconstructions, and for this reason, it is named _image-to-image_. Most of the proposed methods use CNNs, taking as input FBP reconstructions (see, e.g., [11; 12; 13]). The third class is the _plug-and-play_-type approaches, where a network is trained outside of the iterative process and then included within it, thus allowing the iteration to be run indefinitely [14; 15; 16]. The last approach is known as _iterative mapping_, and it is realized through the so-called unrolled (or unfolded) neural networks [17]. The aim of these methods is to mimic the action of a minimization problem by simultaneously learning the hyper-parameters of the model, such as the regularization hyper-parameters, the iterative solution algorithms, and/or the model operators. The first deep unfolding networks were applied to specific inverse problems [18], and they demonstrated improved performance compared to the more traditional optimization algorithms. Since then, deep unfolding has been extended to compressive sensing [19; 20], image deblurring [21], and tomographic image reconstruction. To cite some examples, the first proposals were from [PERSON] and [PERSON] in [22; 23], where they unrolled a proximal primal-dual method. More recent works are: (a) [24], which concerns the fast iterative shrinkage/thresholding algorithm (FISTA), which can be applied to solve CT and electromagnetic tomography reconstruction problems; (b) [25], in which a few iterations of a gradient descent method were applied to a field-of-experts regularized least squares functional; and (c) [26], where the authors unfolded the dual block forward-backward (DBFB) algorithm embedded in an iterative re-weighted scheme for region-of-interest CT image reconstruction. A different scheme is investigated in [27], where the pseudodifferential operator is learned for limited-angle CT.