Sensitivity-Aware Density Estimation in Multiple Dimensions

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 o...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2024-11, Vol.46 (11), p.7120-7135
Main Authors: Boquet-Pujadas, Aleix, Pla, Pol del Aguila, Unser, Michael
Format: Article
Language:English
Subjects:
Bandwidth
Estimation
Hessian-Schatten norm
Imaging
Kernel
PET
rebinning
resampling
Sensitivity
Splines (mathematics)
Weighted density estimation
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Summary: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.
ISSN:0162-8828
1939-3539
1939-3539
2160-9292
DOI:10.1109/TPAMI.2024.3388370