Poisson noise reduction with non-local PCA

Photon-limited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denoising methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio

Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds

Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to learn this mapping directly with plain multi layer perceptrons (MLP) applied to image patches. We will show that by training on large image databases we are able to outperform the current state-of-the-art image denoising methods. In addition, our method achieves results that are superior to one type of theoretical bound and goes a large way toward closing the gap with a second type of theoretical bound. Our approach is easily adapted to less extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG artifacts, salt-and-pepper noise and noise resembling stripes, for which we achieve excellent results as well. We will show that combining a block-matching procedure with MLPs can further improve the results on certain images. In a second paper, we detail the training trade-offs and the inner mechanisms of our MLPs

Sparsity Based Poisson Denoising with Dictionary Learning

The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive i.i.d. Gaussian noise, for which many effective algorithms are available. However, in a low SNR regime, these transformations are significantly less accurate, and a strategy that relies directly on the true noise statistics is required. A recent work by Salmon et al. took this route, proposing a patch-based exponential image representation model based on GMM (Gaussian mixture model), leading to state-of-the-art results. In this paper, we propose to harness sparse-representation modeling to the image patches, adopting the same exponential idea. Our scheme uses a greedy pursuit with boot-strapping based stopping condition and dictionary learning within the denoising process. The reconstruction performance of the proposed scheme is competitive with leading methods in high SNR, and achieving state-of-the-art results in cases of low SNR.Comment: 13 pages, 9 figure

Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope

The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients. We present in this paper an extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension is not a spatial dimension, but the wavelength, the energy, or the time. We show that the MSVST can be used for detecting and characterizing astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to traditional likelihood model fitting, and permits efficient detection across the time dimension and immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_msvst.pd