A new steplength selection for scaled gradient methods with application to image deblurring

Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the steplength parameter defining the descent direction, as in the case of the well-known Barzilai and Borwein rules. In a recent paper, a strategy for the steplength selection approximating the inverse of some eigenvalues of the Hessian matrix has been proposed for gradient methods applied to unconstrained minimization problems. In the quadratic case, this approach is based on a Lanczos process applied every m iterations to the matrix of the most recent m back gradients but the idea can be extended to a general objective function. In this paper we extend this rule to the case of scaled gradient projection methods applied to non-negatively constrained minimization problems, and we test the effectiveness of the proposed strategy in image deblurring problems in both the presence and the absence of an explicit edge-preserving regularization term

On the filtering effect of iterative regularization algorithms for linear least-squares problems

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to provide the fastest methods for the reconstruction of the solution, involving choices of adaptive parameters and scaling matrices. However, in presence of an ill-conditioned model and real data, the need of a regularized solution instead of the least-squares one changed the point of view in favour of iterative algorithms able to combine a fast execution with a stable behaviour with respect to the restoration error. In this paper we want to analyze some classical and recent gradient approaches for the linear least-squares problem by looking at their way of filtering the singular values, showing in particular the effects of scaling matrices and non-negative constraints in recovering the correct filters of the solution

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

Large quadratic programs in training gaussian support vector machines

We consider the numerical solution of the large convex quadratic program arising in training the learning machines named support vector machines. Since the matrix of the quadratic form is dense and generally large, solution approaches based on explicitstorage of this matrix are not practicable. Well known strategies for this quadratic program are based on decomposition techniques that split the problem into a sequence of smaller quadratic programming subproblems. For the solution of these subproblems we present an iterative projection-type method suited for the structure of the constraints and very eective in case of Gaussian support vector machines. We develop an appropriate decomposition technique designed to exploit the high performance of the proposed inner solver on medium or large subproblems. Numerical experiments on large-scale benchmark problems allow to compare this approach with another widelyused decomposition technique. Finally, a parallel extension of the proposed strategy is described

Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy

Gradient projection methods have given rise to effective tools for image deconvolution in several relevant areas, such as microscopy, medical imaging and astronomy. Due to the large scale of the optimization problems arising in nowadays imaging applications and to the growing request of real-time reconstructions, an interesting challenge to be faced consists in designing new acceleration techniques for the gradient schemes, able to preserve the simplicity and low computational cost of each iteration. In this work we propose an acceleration strategy for a state of the art scaled gradient projection method for image deconvolution in microscopy. The acceleration idea is derived by adapting a step-length selection rule, recently introduced for limited-memory steepest descent methods in unconstrained optimization, to the special constrained optimization framework arising in image reconstruction. We describe how important issues related to the generalization of the step-length rule to the imaging optimization problem have been faced and we evaluate the improvements due to the acceleration strategy by numerical experiments on large-scale image deconvolution problems

an automatic procedure based on virtual ergonomic analysis to promote human centric manufacturing

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A comparison of edge-preserving approaches for differential interference contrast microscopy

In this paper we address the problem of estimating the phase from color images acquired with differential-interference-contrast microscopy. In particular, we consider the nonlinear and nonconvex optimization problem obtained by regularizing a least-squares-like discrepancy term with an edge-preserving functional, given by either the hypersurface potential or the total variation one. We investigate the analytical properties of the resulting objective functions, proving the existence of minimum points, and we propose effective optimization tools able to obtain in both the smooth and the nonsmooth case accurate reconstructions with a reduced computational demand

A novel kcna2 variant in a patient with non-progressive congenital ataxia and epilepsy: Functional characterization and sensitivity to 4-aminopyridine

Kv1.2 channels, encoded by the KCNA2 gene, are localized in the central and peripheral nervous system, where they regulate neuronal excitability. Recently, heterozygous mutations in KCNA2 have been associated with a spectrum of symptoms extending from epileptic encephalopathy, intellectual disability, and cerebellar ataxia. Patients are treated with a combination of antiepileptic drugs and 4-aminopyridine (4-AP) has been recently trialed in specific cases. We identified a novel variant in KCNA2, E236K, in a Serbian proband with non-progressive congenital ataxia and early onset epilepsy, treated with sodium valproate. To ascertain the pathogenicity of E236K mutation and to verify its sensitivity to 4-AP, we transfected HEK 293 cells with Kv1.2 WT or E236K cDNAs and recorded potassium currents through the whole-cell patchclamp. In silico analysis supported the electrophysiological data. E236K channels showed voltagedependent activation shifted towards negative potentials and slower kinetics of deactivation and activation compared with Kv1.2 WT. Heteromeric Kv1.2 WT+E236K channels, resembling the condition of the heterozygous patient, confirmed a mixed gain-and loss-of-function (GoF/LoF) biophysical phenotype. 4-AP inhibited both Kv1.2 and E236K channels with similar potency. Homology modeling studies of mutant channels suggested a reduced interaction between the residue K236 in the S2 segment and the gating charges at S4. Overall, the biophysical phenotype of E236K channels correlates with the mild end of the clinical spectrum reported in patients with GoF/LoF defects. The response to 4-AP corroborates existing evidence that KCNA2-disorders could benefit from variant-tailored therapeutic approaches, based on functional studies