Sensitivity-Aware Density Estimation in Multiple Dimensions

TL;DR

This paper introduces a sensitivity-aware density estimation method using spline-based regularization, adaptable to multidimensional data with uneven sampling, and demonstrates its application in PET rebinning.

Contribution

It presents a novel spline-based density estimation framework that incorporates detector sensitivity and promotes sparsity through nuclear norm regularization.

Findings

Method is spatially adaptive and stable against regularization parameter choices.

Successfully tested on standard densities with available software.

Applied to PET rebinning with promising results.

Abstract

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computational speed and flexible boundary conditions offered by splines on a grid. We choose to regularize the Hessian of the spline via the nuclear norm to promote sparsity. As a result, the method is spatially adaptive and stable against the choice of the regularization parameter, which plays the role of the bandwidth. We test our computational pipeline on standard densities and provide software. We also present a new approach to PET rebinning as an application of our framework.