Related papers: First-order convex feasibility algorithms for iter…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
Protocol optimization is critical in Computed Tomography (CT) to achieve high diagnostic image quality while minimizing radiation dose. However, due to the complex interdependencies among CT acquisition and reconstruction parameters,…
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
Compressed sensing (CS) has been introduced to accelerate data acquisition in MR Imaging. However, CS-MRI methods suffer from detail loss with large acceleration and complicated parameter selection. To address the limitations of existing…
Photoacoustic imaging (PAI) suffers from inherent limitations that can degrade the quality of reconstructed results, such as noise, artifacts and incomplete data acquisition caused by sparse sampling or partial array detection. In this…
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…
For reconstructing large tomographic datasets fast, filtered backprojection-type or Fourier-based algorithms are still the method of choice, as they have been for decades. These robust and computationally efficient algorithms have been…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
This article is intended to supplement our 2015 paper in Medical Physics titled "Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization", in which ordered subsets methods were…
Many problems in power systems involve optimizing a certain objective function subject to power flow equations and engineering constraints. A long-standing challenge in solving them is the nonconvexity of their feasible sets. In this paper,…
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…
We analyse some QR decomposition algorithms, and show that the I/O complexity of the tile based algorithm is asymptotically the same as that of matrix multiplication. This algorithm, we show, performs the best when the tile size is chosen…
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…
In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
Low Dose Computed Tomography suffers from a high amount of noise and/or undersampling artefacts in the reconstructed image. In the current article, a Deep Learning technique is exploited as a regularization term for the iterative…