Sensitivity-Aware Density Estimation in Multiple Dimensions
This work addresses density estimation challenges in fields like medical imaging (e.g., PET) by providing a stable, adaptive method, though it appears incremental as it builds on existing spline and regularization techniques.
The authors tackled the problem of estimating probability densities in multidimensional settings with uneven sampling by formulating an optimization problem that incorporates detector sensitivity as a heterogeneous density, using splines for computational efficiency and regularizing with the nuclear norm to promote sparsity, resulting in a spatially adaptive method that is stable against regularization parameter choices. They tested it on standard densities and applied it to PET rebinning.
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.