This paper proposes a deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems in imaging. Traditional iterative methods, while effective, are computationally expensive and require careful hyperparameter selection. The authors observe that unrolled iterative methods can be represented as CNNs when the normal operator of the forward model is a convolution. Based on this, they propose a method that combines direct inversion with a CNN to solve normal-convolutional inverse problems. The CNN is designed to remove artifacts while preserving image structure. The method is tested on sparse-view reconstruction in parallel beam X-ray computed tomography (CT) using synthetic phantoms and real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for more realistic phantoms and can reconstruct a 512×512 image in less than a second on a GPU. The paper discusses inverse problems with shift-invariant normal operators, including denoising, deconvolution, and CT reconstruction. It presents a theory for normal-convolutional operators and describes direct and iterative inversion methods. The proposed method, called FBPCnvNet, combines filtered back projection (FBP) with a CNN trained to regress FBP results to ground truth images. The CNN is based on the U-net architecture with residual learning, allowing it to effectively learn to remove artifacts while preserving image details. Experiments on synthetic and real datasets show that the proposed method outperforms state-of-the-art iterative reconstruction methods, particularly in preserving fine details. The method is applicable to various imaging modalities, including CT, MRI, and diffraction tomography. However, the method has limitations in transferring between datasets and requires retraining for different subsampling factors. The paper concludes that the proposed method is well-suited for solving inverse problems with shift-invariant normal operators, particularly in biomedical imaging.This paper proposes a deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems in imaging. Traditional iterative methods, while effective, are computationally expensive and require careful hyperparameter selection. The authors observe that unrolled iterative methods can be represented as CNNs when the normal operator of the forward model is a convolution. Based on this, they propose a method that combines direct inversion with a CNN to solve normal-convolutional inverse problems. The CNN is designed to remove artifacts while preserving image structure. The method is tested on sparse-view reconstruction in parallel beam X-ray computed tomography (CT) using synthetic phantoms and real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for more realistic phantoms and can reconstruct a 512×512 image in less than a second on a GPU. The paper discusses inverse problems with shift-invariant normal operators, including denoising, deconvolution, and CT reconstruction. It presents a theory for normal-convolutional operators and describes direct and iterative inversion methods. The proposed method, called FBPCnvNet, combines filtered back projection (FBP) with a CNN trained to regress FBP results to ground truth images. The CNN is based on the U-net architecture with residual learning, allowing it to effectively learn to remove artifacts while preserving image details. Experiments on synthetic and real datasets show that the proposed method outperforms state-of-the-art iterative reconstruction methods, particularly in preserving fine details. The method is applicable to various imaging modalities, including CT, MRI, and diffraction tomography. However, the method has limitations in transferring between datasets and requires retraining for different subsampling factors. The paper concludes that the proposed method is well-suited for solving inverse problems with shift-invariant normal operators, particularly in biomedical imaging.