Designing Sampling Schemes for Multi-Dimensional Data

TL;DR

This paper introduces a convex optimization-based method for designing non-uniform sampling schemes in multi-dimensional data, optimizing parameter estimation accuracy while allowing flexible parameter importance and prior knowledge integration.

Contribution

It presents a novel convex optimization framework for sampling scheme design that minimizes the Cramér-Rao bound considering parameter importance and prior information.

Findings

Numerical examples demonstrate the scheme's efficiency.

The method effectively incorporates prior knowledge.

Optimizes sampling for improved parameter estimation.

Abstract

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cram\'er-Rao lower bound for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme.