Anisotropic local likelihood approximations: theory, algorithms, applications

We consider a signal restoration from observations corrupted by random noise. The local maximum likelihood technique allows to deal with quite general statistical models of signal dependent observations, relaxes the stan- dard parametric modelling of the standard maximum likelihood, and results in ßexible nonparametric regression estimation of the signal. We deal with the anisotropy of the signal using multi-window directional sectorial local polynomial approximation. The data-driven sizes of the sectorial windows, obtained by the intersection of conÞdence interval (ICI) algorithm, allow to form starshaped adaptive neighborhoods used for the pointwise estimation. The developed approach is quite general and is applicable for multivariable data. A fast adaptive algorithm implementation is proposed. It is applied for photon-limited imaging with the Poisson distribution of data. Simulation experiments and comparison with some of the best results in the Þeld demonstrate an advanced performance of the developed algorithms.