Generalized sampling: a variational approach .I. Theory

Generalized Sampling: A Variational Approach. Part I: Theory

We consider the problem of reconstructing a multidimensional vector function f in : R → R from a finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an a priori given space; e.g., the space of bandlimited functions. Instead, we have chosen to specify a reconstruction that is optimal in the sense of a quadrati...

Generalized Sampling: A Variational Approach

We consider the problem of reconstructing a multidimensional and multivariate function f : R → R from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which reconstruct the function in some signal space V , our reconstruction is optimal in the sense of a plausibility criterion J . The reconstruction is either consistent with the...

Generalized sampling: a variational approach .II. Applications

The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formula...

Multiobjective Variational Programming under Generalized Vector Variational Type I Invexity

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

Variational Approach to Retinex Theory