Deep Radon Prior: A Fully Unsupervised Framework for Sparse-View CT Reconstruction

Although sparse-view computed tomography (CT) has significantly reduced radiation dose, it also introduces severe artifacts which degrade the image quality. In recent years, deep learning-based methods for inverse problems have made remarkable progress and have become increasingly popular in CT reconstruction. However, most of these methods suffer several limitations: dependence on high-quality training data, weak interpretability, etc. In this study, we propose a fully unsupervised framework called Deep Radon Prior (DRP), inspired by Deep Image Prior (DIP), to address the aforementioned limitations. DRP introduces a neural network as an implicit prior into the iterative method, thereby realizing cross-domain gradient feedback. During the reconstruction process, the neural network is progressively optimized in multiple stages to narrow the solution space in radon domain for the under-constrained imaging protocol, and the convergence of the proposed method has been discussed in this work. Compared with the popular pre-trained method, the proposed framework requires no dataset and exhibits superior interpretability and generalization ability. The experimental results demonstrate that the proposed method can generate detailed images while effectively suppressing image artifacts.Meanwhile, DRP achieves comparable or better performance than the supervised methods.Comment: 11 pages, 12 figures, Journal pape

Fractal Compressive Sensing

This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and one-dimensional (1D) trajectories derived from the discrete Radon transform (DRT). Unlike radial trajectories, DRT projections can be back-projected without interpolation. Thus, we also propose a novel reconstruction method based on the exact projections of the DRT called finite Fourier reconstruction (FFR). We term this combined p.frac and FFR strategy, finite compressive sensing (FCS), with image recovery demonstrated on experimental and simulated data; image quality comparisons are made with Cartesian random sampling in 1D and two-dimensional (2D), as well as radial under-sampling in a more constrained experiment. Our experiments indicate FCS enables 3-5dB gain in peak signal-to-noise ratio (PSNR) for 2-, 4- and 8-fold under-sampling compared to 1D Cartesian random sampling. This paper aims to: Review common sampling strategies for compressed sensing (CS)-magnetic resonance imaging (MRI) to inform the motivation of a projective and Cartesian sampling scheme. Compare the incoherence of these sampling strategies and the proposed p.frac. Compare reconstruction quality of the sampling schemes under various reconstruction strategies to determine the suitability of p.frac for CS-MRI. It is hypothesised that because p.frac is a highly incoherent sampling scheme, that reconstructions will be of high quality compared to 1D Cartesian phase-encode under-sampling.Comment: 12 pages, 10 figures, 1 tabl

Chaotic Iterative Algorithms for Image Reconstruction from Incomplete Projection Data

The problem of computer tomography is considered from incomplete projection data with chaotic algorithms for some particular systems of reconstruction. The numerical reconstruction algorithms and numerical simulation results are presented for a number of modeling objects which can be described by means of discrete functions.Рассмотрена задача компьютерной томографии по неполным проекционным данным с использованием хаотических алгоритмов для некоторых специальных систем восстановления. Представлены численные алгоритмы восстановления и результаты численного моделирования для ряда моделируемых объектов, которые могут быть описаны посредством дискретных функций.Розглянуто задачу комп’ютерної томографії по неповним проективним даним з використанням хаотичних алгоритмів для деяких спеціальних систем відновлення. Наведено числові алгоритми відновлення та результати числового моделювання для об’єктів, які можуть бути описані дискретними функціями

Block-Parallel Chaotic Algorithms for Image Reconstruction

The paper is devoted to the elaboration and implementation of block-parallel asynchronous algorithms for computer tomography. The numerical reconstruction algorithms and numerical simulation results for a number of modeling objects and some particular systems of reconstruction are presented.Разработаны и выполнены блочно-параллельные алгоритмы компьютерной томографии.Представлены численные алгоритмы восстановления и результаты численного моделирования для ряда тестовых задач и некоторых частных случаев систем реконструкции сбора данных.Розроблено та виконано блочно-паралельні алгоритми комп’ютерної томографії. Наведено чисельні алгоритми відновлення та результати чисельного моделювання для тестових задач і деяких окремих випадків систем реконструкції збирання даних

Overview of compressed sensing: Sensing model, reconstruction algorithm, and its applications

With the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist-Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials. © 2020 by the authors

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future

Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies

The core components (e.g. fuel assemblies, spacer grids, control rods) of the nuclear reactors encounter harsh environment due to high temperature, physical stress, and a tremendous level of radiation. The integrity of these elements is crucial for safe operation of the nuclear power plants. The Post Irradiation Examination (PIE) can reveal information about the integrity of the elements during normal operations and off‐normal events. Computed tomography (CT) is a tool for evaluating the structural integrity of elements non-destructively. CT requires many projections to be acquired from different view angles after which a mathematical algorithm is adopted for reconstruction. Obtaining many projections is laborious and expensive in nuclear industries. Reconstructions from a small number of projections are explored to achieve faster and cost-efficient PIE. Classical reconstruction algorithms (e.g. filtered back projection) cannot offer stable reconstructions from few projections and create severe streaking artifacts. In this thesis, conventional algorithms are reviewed, and new algorithms are developed for reconstructions of the nuclear fuel assemblies using few projections. CT reconstruction from few projections falls into two categories: the sparse-view CT and the limited-angle CT or tomosynthesis. Iterative reconstruction algorithms are developed for both cases in the field of compressed sensing (CS). The performance of the algorithms is assessed using simulated projections and validated through real projections. The thesis also describes the systematic strategy towards establishing the conditions of reconstructions and finds the optimal imaging parameters for reconstructions of the fuel assemblies from few projections. --Abstract, page iii