Multiple Measurement Vector Based Complex-Valued Multi-Frequency ECT

omplex-Valued, Multi-Frequency Electrical Capacitance Tomography (CVMF-ECT) is a recently developed tomographic concept which is capable to simultaneously reconstruct spectral permittivity and conductivity properties of target objects within the region of interest. To date, this concept has been limited to simulation and another key issue restricting its wide adoption lies in its poor image quality. This paper reports a CVMF-ECT system to verify its practical feasibility and further proposes a novel image reconstruction framework to effectively and efficiently reconstruct multi-frequency images using complex-valued capacitance data. The image reconstruction framework utilizes the inherent spatial correlations of the multi-frequency images as a priori information and encodes it by using Multiple Measurement Vector (MMV) model. Alternating direction method of multipliers was introduced to solve the MMV problem. Real-world experiments validate the feasibility of CVMF-ECT, and MMV based CVMF-ECT method demonstrates superior performance compared to conventional ECT approaches

Steplength selection in gradient projection methods for box-constrained quadratic programs

The role of the steplength selection strategies in gradient methods has been widely in- vestigated in the last decades. Starting from the work of Barzilai and Borwein (1988), many efficient steplength rules have been designed, that contributed to make the gradient approaches an effective tool for the large-scale optimization problems arising in important real-world applications. Most of these steplength rules have been thought in unconstrained optimization, with the aim of exploiting some second-order information for achieving a fast annihilation of the gradient of the objective function. However, these rules are successfully used also within gradient projection methods for constrained optimization, though, to our knowledge, a detailed analysis of the effects of the constraints on the steplength selections is still not available. In this work we investigate how the presence of the box constraints affects the spectral properties of the Barzilai\u2013Borwein rules in quadratic programming problems. The proposed analysis suggests the introduction of new steplength selection strategies specifically designed for taking account of the active constraints at each iteration. The results of a set of numerical experiments show the effectiveness of the new rules with respect to other state of the art steplength selections and their potential usefulness also in case of box-constrained non-quadratic optimization problems

A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization

Funding Information: The first author was financially supported by FGV (Fundação Getulio Vargas) through the excellence post–doctoral fellowship program. The second author was financially supported by FAPESP (Projects 2013/05475-7 and 2017/18308-2) and CNPq (Project 301888/2017-5). The third author was financially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We introduce a family of weighted conjugate-gradient-type methods, for strictly convex quadratic functions, whose parameters are determined by a minimization model based on a convex combination of the objective function and its gradient norm. This family includes the classical linear conjugate gradient method and the recently published delayed weighted gradient method as the extreme cases of the convex combination. The inner cases produce a merit function that offers a compromise between function-value reduction and stationarity which is convenient for real applications. We show that each one of the infinitely many members of the family exhibits q-linear convergence to the unique solution. Moreover, each one of them enjoys finite termination and an optimality property related to the combined merit function. In particular, we prove that if the n × n Hessian of the quadratic function has p < n different eigenvalues, then each member of the family obtains the unique global minimizer in exactly p iterations. Numerical results are presented that demonstrate that the proposed family is promising and exhibits a fast convergence behavior which motivates the use of preconditioning strategies, as well as its extension to the numerical solution of general unconstrained optimization problems.publishersversionpublishe

A Coordinate Descent Method for Total Variation Minimization

Total variation (TV) is a well-known image model with extensive applications in various images and vision tasks, for example, denoising, deblurring, superresolution, inpainting, and compressed sensing. In this paper, we systematically study the coordinate descent (CoD) method for solving general total variation (TV) minimization problems. Based on multidirectional gradients representation, the proposed CoD method provides a unified solution for both anisotropic and isotropic TV-based denoising (CoDenoise). With sequential sweeping and small random perturbations, CoDenoise is efficient in denoising and empirically converges to optimal solution. Moreover, CoDenoise also delivers new perspective on understanding recursive weighted median filtering. By incorporating with the Augmented Lagrangian Method (ALM), CoD was further extended to TV-based image deblurring (ALMCD). The results on denoising and deblurring validate the efficiency and effectiveness of the CoD-based methods

Mechanistic Understanding of Co-crystal solubility and dissolution by using a combination of Experimental and Molecular Modelling Techniques

The purpose of this study is to improve the solubility, dissolution rate and permeability of poorly water-soluble drugs by understanding the mechanism of dissolution at molecular level of Flufenamic acid and Carbamazepine co-crystals in the presence of polymers. This study has been separated into four sections: (1) Formation of pharmaceutical co-crystals: Three pharmaceutical co-crystals of poorly water soluble active pharmaceutical ingredient (API) of Flufenamic acid (FFA) and Carbamazepine (CBZ) were synthesized, including 1:1 Flufenamic acid-theophylline co-crystal (FFATP CO), 1:1 Flufenamic acid-nicotinamide co-crystal (FFA-NIC CO) and 1:1 Carbamazepine-nicotinamide co-crystal (CBZ-NIC CO). The results of Fourier Transform Infrared spectroscopy (FTIR), Differential scanning calorimetry (DSC) and X-ray Powder Diffraction (XRPD) confirmed the formation of co-crystals. (2) The effect of polymers on the surface dissolution of co-crystals: The influence of three polymers (polyethylene glycol (PEG), polyvinylpyrrolidone (PVP), and a copolymer of N-vinly-2- pyrrolidone (60%) and vinyl acetate (40%) (PVP-VA)) on the surfaces of FFA-TP CO, FFA-NIC CO and CBZ-NIC CO was studied using Atomic force Microscopy (AFM), Scanning electron microscopy (SEM) and Raman spectroscopy. It was found that the co-crystals have different dissolution mechanisms, and that addition of polymers can alter the dissolution properties of co-crystals by interacting with the crystal faces. (3) The molecular interactions between the drugs, co-formers and polymers were investigated using Nuclear Magnetic Resonance (NMR) and Diffusion Ordered Spectroscopy (DOSY). It was found that the type of a polymer, its concentration, and the interaction of the polymer with a co-former in solution will significantly affect the FFA and CBZ co-crystals (4). Molecular modelling of free drug molecules with coformers and polymers in the presence of water molecules: Results indicate bulk precipitation could be occurring for FFA molecules in solution and that PVP-VA was an effective precipitation inhibitor for all three co-crystals studied in solution. Overall, PVP was an effective polymer for surface precipitation inhibitor and PVP-VA was the most effective inhibitor for precipitation in solution