Quantum median filter for total variation image denoising

In this new computing paradigm, named quantum computing, researchers from all over the world are taking their first steps in designing quantum circuits for image process- ing, through a difficult process of knowledge transfer. This effort is named quantum image processing, an emerging research field pushed by powerful parallel comput- ing capabilities of quantum computers. This work goes in this direction and proposes the challenging development of a powerful method of image denoising, such as the total variation (TV) model, in a quantum environment. The proposed quantum TV is described and its sub-components are analysed. Despite the natural limitations of the current capabilities of quantum devices, the experimental results show a competitive denoising performance compared to the classical variational TV counterpar

MOLECULAR COMPOSITION OF ACTIVE CHIOS MASTIC GUM COMPOUNDS, TERPENES, FOR USE IN COSMETIC, NUTRACEUTICAL, MEDICAL DEVICES AND PHARMACEUTICAL APPLICATIONS.

Chios mastic gum is a resin generated by the plant Pistacia lentiscus var. chia, generally cultivated in Mediterranean countries and particularly in the southern part of the Greek island of Chios. P. lentiscus is a very ancient plant and the related gum has been used since many centuries. Recent studies have associated specific pharmaceutical properties of Chios mastic gum with its particular molecular components. In fact, increasing scientific evidences are available on the therapeutic activity of Chios mastic gum. Its gastro-intestinal, antioxidant, anti-inflammatory, antidiabetic, antimicrobial and anticancer activity, as well as its beneficial effects in oral hygiene and in skin care are largely documented. In particular, it is used as a seasoning in Mediterranean cuisine, in the production of chewing gum, in perfumery, in dentistry, and for the relief of epigastric pain and protection against peptic ulcer. Up to more than 70 constituents of Chios mastic gum have been found and more than 60 have been identified. Six components, namely α-pipene, β-pipene, β-myrcene, linalool, trans-caryophyllene and camphene, account for 65% to 80% of the weight of the Chios mastic gum. The active components contributing to its therapeutic effects belong to the class of terpenes (mono- and sesquiterpenoids, triterpenic acids and triterpenoids). Triterpenic acids, in particular, possess various biological capacities such as anti-inflammatory, antioxidant, antiatherogenic, antihyperlipidemic, anti-tumor, antidiabetic and hepatoprotective effects. Chios mastic gum has been demonstrated to contain many of these active molecules such as oleanonic acid, moronic acid, 24Z-masticadienonic acid, 24Z-isomasticadienonic acid, 24Z-masticadienolic acid, 24Z-isomasticadienolic acid

Variability in genes regulating vitamin D metabolism is associated with vitamin D levels in type 2 diabetes

Mortality rate is increased in type 2 diabetes (T2D). Low vitamin D levels are associated with increased mortality risk in T2D. In the general population, genetic variants affecting vitamin D metabolism (DHCR7 rs12785878, CYP2R1 rs10741657, GC rs4588) have been associated with serum vitamin D. We studied the association of these variants with serum vitamin D in 2163 patients with T2D from the "Sapienza University Mortality and Morbidity Event Rate (SUMMER) study in diabetes". Measurements of serum vitamin D were centralised. Genotypes were obtained by Eco™ Real-Time PCR. Data were adjusted for gender, age, BMI, HbA1c, T2D therapy and sampling season. DHCR7 rs12785878 (p = 1 x 10-4) and GC rs4588 (p = 1 x 10-6) but not CYP2R1 rs10741657 (p = 0.31) were significantly associated with vitamin D levels. One unit of a weighted genotype risk score (GRS) was strongly associated with vitamin D levels (p = 1.1 x 10-11) and insufficiency (<30 ng/ml) (OR, 95%CI = 1.28, 1.16-1.41, p = 1.1 x 10-7). In conclusion, DHCR7 rs12785878 and GC rs4588, but not CYP2R1 rs10741657, are significantly associated with vitamin D levels. When the 3 variants were considered together as GRS, a strong association with vitamin D levels and vitamin D insufficiency was observed, thus providing robust evidence that genes involved in vitamin D metabolism modulate serum vitamin D in T2D

Blind cluster structured sparse signal recovery: A nonconvex approach

open3noWe consider the problem of recovering a sparse signal when its nonzero coefficients tend to cluster into blocks, whose number, dimension and position are unknown. We refer to this problem as {it blind cluster structured sparse recovery}. For its solution, differently from the existing methods that consider the problem in a statistical context, we propose a deterministic neighborhood based approach characterized by the use both of a nonconvex, nonseparable sparsity inducing function and of a penalized version of the iterative $ell_1$ reweighted method. Despite the high nonconvexity of the approach, a suitable integration of these building elements led to the development of MB-NFCS ({it Model Based Nonlinear Filtering for Compressed Sensing}), an iterative fast, self-adaptive, and efficient algorithm that, without requiring any information on the sparsity pattern, adjusts at each iteration the action of the sparsity inducing function in order to strongly encourage the emerging cluster structure. The effectiveness of the proposed approach is demonstrated by a large set of numerical experiments that show the superior performance of MB-NFCS to the state-of-the-art algorithms.This work was supported by Miur, R.F.O. projects.openDamiana Lazzaro;Laura B. Montefusco;Serena PapiDamiana Lazzaro;Laura B. Montefusco;Serena Pap

Matrix completion for matrices with low-rank displacement. ETNA - Electronic Transactions on Numerical Analysis

The matrix completion problem consists in the recovery of a low-rank or approximately low-rank matrix from a sampling of its entries. The solution rank is typically unknown, and this makes the problem even more challenging. However, for a broad class of interesting matrices with so-called displacement structure, the originally ill-posed completion problem can find an acceptable solution by exploiting the knowledge of the associated displacement rank. The goal of this paper is to propose a variational non-convex formulation for the low-rank matrix completion problem with low-rank displacement and to apply it to important classes of medium-large scale structured matrices. Experimental results show the effectiveness and efficiency of the proposed approach for Toeplitz and Hankel matrix completion problems

A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography

Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However, the linearized problem is only a rough approximation of the real situation, where the measurements can further contain unavoidable noise. The proposed reconstruction variational framework allows to turn the complete nonlinear ill-posed EIT problem into a sequence of regularized linear least squares optimization problems via a forward-backward splitting strategy, thus converting the ill-posed problem to a well-posed one. The framework can easily integrate suitable penalties to enforce smooth or piecewise-constant conductivity reconstructions depending on prior information. Numerical experiments validate the effectiveness and feasibility of the proposed approach

A Robust Group-Sparse Representation Variational Method with applications to Face Recognition

In this paper we propose a Group-Sparse Representation based method with applications to Face Recognition (GSR-FR). The novel sparse representation variational model includes a non-convex sparsity-inducing penalty and a robust non-convex loss function. The penalty encourages group sparsity by using approximation of the \u21130-quasinorm, and the loss function is chosen to make the algorithm robust to noise, occlusions and disguises. The solution of the non-trivial non-convex optimization problem is efficiently obtained by a majorization-minimization strategy combined with forward-backward splitting, which in particular reduces the solution to a sequence of easier convex optimization sub-problems. Extensive experiments on widely used face databases show the potentiality of the proposed model and demonstrate that the GSR-FR algorithm is competitive with state-of-the-art methods based on sparse representation, especially for very low dimensional feature spaces

A fast algorithm for nonconvex approaches to sparse recovery problems

This paper addresses the problem of sparse signal recovery from a lower number of measurements than those requested by the classical compressed sensing theory. This problem is formalized as a constrained minimization problem, where the objective function is nonconvex and singular at the origin. Several algorithms have been recently proposed, which rely on iterative reweighting schemes, that produce better estimates at each new minimization step. Two such methods are iterative reweighted l2 and l1 minimization that have been shown to be effective and general, but very computationally demanding. The main contribution of this paper is the proposal of the algorithm WNFCS, where the reweighted schemes represent the core of a penalized approach to the solution of the constrained nonconvex minimization problem. The algorithm is fast, and succeeds in exactly recovering a sparse signal from a smaller number of measurements than the l1 minimization and in a shorter time. WNFCS is very general, since it represents an algorithmic framework that can easily be adapted to different reweighting strategies and nonconvex objective functions. Several numerical experiments and comparisons with some of the most recent nonconvex minimization algorithms confirm the capabilities of the proposed algorithm