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This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…

An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform…

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we…

Compressed sensing Synthetic Aperture Radar (SAR) image formation, formulated as an inverse problem and solved with traditional iterative optimization methods can be very computationally expensive. We investigate the use of denoising…

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors…

Metal artifact reduction (MAR) is a challenging problem in computed tomography (CT) imaging. A popular class of MAR methods replace sinogram measurements that are corrupted by metal with artificial data. While these ``projection…

Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…

We propose a new deterministic Kaczmarz algorithm for solving consistent linear systems $A\mathbf{x}=\mathbf{b}$. Basically, the algorithm replaces orthogonal projections with reflections in the original scheme of Stefan Kaczmarz. Building…

The randomized Kaczmarz methods are a popular and effective family of iterative methods for solving large-scale linear systems of equations, which have also been applied to linear feasibility problems. In this work, we propose a new block…

The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…

The Kaczmarz method is an efficient iterative algorithm for large-scale linear systems. However, its linear convergence rate suffers from ill-conditioned problems and is highly sensitive to the smallest nonzero singular value. In this work,…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Based on the Scale-Splitting (SCSP) iteration method presented by Hezari et al. in (A new iterative method for solving a class of complex symmetric system linear of equations, Numerical Algorithms 73 (2016) 927-955), we present a new…

Model-Based Image Reconstruction (MBIR) methods significantly enhance the quality of computed tomographic (CT) reconstructions relative to analytical techniques, but are limited by high computational cost. In this paper, we propose a…

Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…

We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…

The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…