1,876 research outputs found
Newton-MR: Inexact Newton Method With Minimum Residual Sub-problem Solver
We consider a variant of inexact Newton Method, called Newton-MR, in which
the least-squares sub-problems are solved approximately using Minimum Residual
method. By construction, Newton-MR can be readily applied for unconstrained
optimization of a class of non-convex problems known as invex, which subsumes
convexity as a sub-class. For invex optimization, instead of the classical
Lipschitz continuity assumptions on gradient and Hessian, Newton-MR's global
convergence can be guaranteed under a weaker notion of joint regularity of
Hessian and gradient. We also obtain Newton-MR's problem-independent local
convergence to the set of minima. We show that fast local/global convergence
can be guaranteed under a novel inexactness condition, which, to our knowledge,
is much weaker than the prior related works. Numerical results demonstrate the
performance of Newton-MR as compared with several other Newton-type
alternatives on a few machine learning problems.Comment: 35 page
Mesh-to-raster based non-rigid registration of multi-modal images
Region of interest (ROI) alignment in medical images plays a crucial role in
diagnostics, procedure planning, treatment, and follow-up. Frequently, a model
is represented as triangulated mesh while the patient data is provided from CAT
scanners as pixel or voxel data. Previously, we presented a 2D method for
curve-to-pixel registration. This paper contributes (i) a general
mesh-to-raster (M2R) framework to register ROIs in multi-modal images; (ii) a
3D surface-to-voxel application, and (iii) a comprehensive quantitative
evaluation in 2D using ground truth provided by the simultaneous truth and
performance level estimation (STAPLE) method. The registration is formulated as
a minimization problem where the objective consists of a data term, which
involves the signed distance function of the ROI from the reference image, and
a higher order elastic regularizer for the deformation. The evaluation is based
on quantitative light-induced fluoroscopy (QLF) and digital photography (DP) of
decalcified teeth. STAPLE is computed on 150 image pairs from 32 subjects, each
showing one corresponding tooth in both modalities. The ROI in each image is
manually marked by three experts (900 curves in total). In the QLF-DP setting,
our approach significantly outperforms the mutual information-based
registration algorithm implemented with the Insight Segmentation and
Registration Toolkit (ITK) and Elastix
Cdma blind channel equalization: a weighted subsface a proach
This paper considers the problem of blind demodulation of multiuser information symbols in a direct-sequence code-division multiple access (DS-CDMA) environment. Channel estimation and symbol detection in the presence of both multiple access interference (MAI) and intersymbol interference (ISI) is carried out with second order statistics methods from the received data. This problem is similar to direction of arrival (DOA) estimation, where many solutions like the MUSIC algorithm orPeer ReviewedPostprint (published version
Flexible modification of Gauss--Newton method and its stochastic extension
This work presents a novel version of recently developed Gauss--Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global convergence bounds and under natural non-degeneracy assumptions we present local quadratic convergence results. We developed stochastic optimization algorithms for presented Gauss--Newton method and justified sub-linear and linear convergence rates for these algorithms using weak growth condition (WGC) and Polyak--Lojasiewicz (PL) inequality. We show that Gauss--Newton method in stochastic setting can effectively find solution under WGC and PL condition matching convergence rate of the deterministic optimization method. The suggested method unifies most practically used Gauss--Newton method modifications and can easily interpolate between them providing flexible and convenient method easily implementable using standard techniques of convex optimization
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