Dynamic Sampling Schemes for Optimal Noise Learning Under Multiple Nonsmooth Constraints
نویسندگان
چکیده
We consider the bilevel optimisation approach proposed in [5] for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way.
منابع مشابه
Randomized Block Subgradient Methods for Convex Nonsmooth and Stochastic Optimization
Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging ([22, 36]), we present stochastic block dual averaging (SBDA)—a novel class of block subgradient methods for convex nonsmooth and stochastic optimization. SBDA re...
متن کاملImportance Sampling for Multiscale Diffusions
We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient...
متن کاملSolving Multiple Fuels Dynamic Environmental/Economic Dispatch Problem and Incentive Based Demand Response Considering Spinning Reserve Requirements
In this paper a new integrated model of the dynamic environmental/economic dispatch (DEED) problem and emergency demand response program (EDRP) has been presented by which their interactions are investigated. DEED schedules the online generators power output over the whole dispatch period subject to some practical constraints so that the fuel costs and emission are optimized simultaneously. EDR...
متن کاملRoundoff Noise Minimization of State-Space Digital Filters Using Separate and Joint Error Feedback/Coordinate Transformation Optimization
This paper investigates the problem of minimizing roundoff noise under 2-norm dynamic-range scaling constraints in state-space digital filters by means of error feedback as well as joint error feedback/coordinate transformation optimization. First, several techniques for the determination of optimal full-scale, diagonal, and scalar error-feedback matrices for a given state-space digital filter ...
متن کاملOPTIMAL NOZZLE SHAPES OF CO2-N2-H2O GASDYNAMIC LASERS
In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...
متن کامل