Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal

By Bo Zhang, Mohamed-Jalal Fadili, Jean-Luc Starck. IEEE Transactions on Image Processing, 2008

386 citations recorded by the source corpus.

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes. By doing so, the noise-contaminated coefficients of these MS-VST-modified transforms are asymptotically normally distributed with known variances. A classical hypothesis-testing framework is adopted to detect the significant coefficients, and a sparsity-driven iterative scheme reconstructs properly the final estimate. A range of examples show the power of this MS-VST approach for recovering important structures of various morphologies in (very) low-count images. These results also demonstrate that the MS-VST approach is competitive relative to many existing denoising methods.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/1b6b70e5168836f61fb300d9fe3667b99f66804b

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Citations in the corpus

The Curvelet Transform (2010, methodology): “[69] used curvelets for Poisson noise removal in comparison with wavelets and ridgelets.”
The SURE-LET Approach to Image Denoising (2007, result): “We obtain similar results to the Platelet method, which was shown to be competitive with the recent approach described in [159].”
Poisson Noise Reduction with Non-local PCA (2012, methodology): “Simply transforming Poisson data to produce data with approximate Gaussian noise (via, for instance, the variance stabilizing Anscombe transform [2, 31] or Fisz transform [17, 18]) can be effective when the number photon counts are uniformly high [5, 46].”
Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences (2010, methodology): “frame separately without using the temporal redundancy of image series [12], [13].”
Image deblurring with Poisson data: from cells to galaxies (2009, methodology): “The denoising of Poisson data, based on wavelet or similar transforms, is, in general, performed after a preprocessing consisting in the use of transforms able to stabilize the variance of the noise, such as the Anscombe transform or generalizations of it [9, 138].”
Image Denoising in Mixed Poisson–Gaussian Noise (2011, methodology): “…the contributions of Jansen, who combined VST with multiscale Bayesian models [29], and Zhang et al. who proposed a multiscale VST that can better stabilize very low intensity signals, and showed how it can be efficiently used with the latest multiresolution transformations (e.g., curvelets) [30].”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, methodology): “[41] proposed more sophisticated variance stabilizing transforms applied on filtered Poisson processes.”
This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms—Theory and Practice (2010, methodology): “In a more recent work, Zhang et al. [22] propose a multiscale variance-stabilizing transform (MSVST) which applies a VST to the empirical wavelet, ridgelet or curvelet transform coefﬁcients.”