MiniMax Methods for Image Reconstruction
MiniMax Methods for Image Reconstruction
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Multiscale Reconstruction of Photon-Limited Hyperspectral Data
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging
IEEE Transactions on Information Theory
A statistical multiscale framework for Poisson inverse problems
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Multiscale Poisson Intensity and Density Estimation
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal
IEEE Transactions on Image Processing
Compressed sensing performance bounds under Poisson noise
IEEE Transactions on Signal Processing
Poisson Noise Reduction with Non-local PCA
Journal of Mathematical Imaging and Vision
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This paper studies photon-limited spectral intensity estimation and proposes a spatially and spectrally adaptive, nonparametric method for estimating spectral intensities from Poisson observations. Specifically, our method searches through estimates defined over a family of recursive dyadic partitions in both the spatial and spectral domains, and finds the one that maximizes a penalized log likelihood criterion. The key feature of this approach is that the partition cells are anisotropic across the spatial and spectral dimensions, so that the method adapts to varying degrees of spatial and spectral smoothness, even when the respective degrees of smoothness are not known a priori. The proposed approach is based on the key insight that spatial boundaries and singularities exist in the same locations in every spectral band, even though the contrast or perceptibility of these features may be very low in some bands. The incorporation of this model into the reconstruction results in significant performance gains. Furthermore, for spectral intensities that belong to the anisotropic -Besov function class, the proposed approach is shown to be near-minimax optimal. The upper bounds on the risk function, which is the expected squared Hellinger distance between the true intensity and the estimate obtained using the proposed approach, matches the best possible lower bound up to a log factor for certain degrees of spatial and spectral smoothness. Experiments conducted on realistic data sets show that the proposed method can reconstruct the spatial and the spectral inhomogeneities very well even when the observations are extremely photon-limited (i.e., less than 0.1 photon per voxel).