4 research outputs found
Improvements on "Fast space-variant elliptical filtering using box splines"
It is well-known that box filters can be efficiently computed using
pre-integrations and local finite-differences
[Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining
it with a non-standard variant of the Central Limit Theorem, a constant-time or
O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform
space-variant filtering using Gaussian-like kernels. The algorithm was based on
the observation that both isotropic and anisotropic Gaussians could be
approximated using certain bivariate splines called box splines. The attractive
feature of the algorithm was that it allowed one to continuously control the
shape and size (covariance) of the filter, and that it had a fixed
computational cost per pixel, irrespective of the size of the filter. The
algorithm, however, offered a limited control on the covariance and accuracy of
the Gaussian approximation. In this work, we propose some improvements by
appropriately modifying the algorithm in [Chaudhury2010].Comment: 7 figure
Sparsity-Driven Reconstruction for FDOT With Anatomical Priors
In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical regions where the fluorescent probe has accumulated, and second, a regularization effect inside the selected anatomical regions. After formulating the reconstruction in a variational framework, we analyze the resulting optimization problem and derive a practical numerical method tailored to (2, 1)-mixed-norm regularization. The proposed method includes as particular cases other sparsity promoting regularization methods such as -norm penalization and total variation penalization. Results on synthetic and experimental data are presented