Least-squares methods with Poissonian noise: an analysis and a comparison with the Richardson-Lucy algorithm

The impulsive noise in astronomical images originates from various sources. It develops as a result of thermal generation in pixels, collision of cosmic rays with image sensor or may be induced by high readout voltage in Electron Multiplying CCD (EMCCD). It is usually efficiently removed by employing the dark frames or by averaging several exposures. Unfortunately, there are some circumstances, when either the observed objects or positions of impulsive pixels evolve and there...

We describe a rapid and direct method for regularizing, post-facto, the point-spread function (PSF) of a telescope or other imaging instrument, across its entire field of view. Imaging instruments in general blur point sources of light by local convolution with a point-spread function that varies slowly across the field of view, due to coma, spherical aberration, and similar effects. It is possible to regularize the PSF in post-processing, producing data with a homogeneous ``...

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key innovations are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a non-linear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minim...

This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given and the issues arising from sparse Fourier data are discussed. The effects of various regularizations are described. In the proposed general framework, most existing algorithms can be understood. For an astronomer, such an understanding is crucial not only for selecting and using an algorithm but also to ensure...

The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based regularizers involve the popular total variation semi-norm have become standard techniques for Poisson image restoration due to its edge-preserving ability. Various efficient algorithms have been developed for solving the corresponding minimization...

In this article, we propose a variational PDE model using $\ell_2-\ell_p$ regulariser for removing Poisson noise in presence of blur. The proposed minimization problem is solved using augmented Lagrangian method. The convergence of the sequence of minimizers have been carried out. Numerical simulations on some standard test images have been shown. The numerical results are compared with that of a few models existed in literature in terms of image quality metric such as SSIM, ...

We present an application of the Richardson-Lucy algorithm to the analysis of color-magnitude diagrams by converting the CMD into an image and using a restoring point spread function function ({\it psf}) derived from the known, often complex, sources of error. We show numerical experiments that demonstrate good recovery of the original image and establish convergence rates for ideal cases with single gaussian uncertainties and poisson noise using a $\chi^2$ statistic. About 3...

We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the bserved image. But in contract to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some "oracle" weights are defined by minimizing a very tight upper bound of the Mean Square Error. For a practical application the we...

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The Poisson--Gaussian noise leads to a weighted minimization problem, with solution-dependent weights. To address outliers, the standard least squares fit-to-data metric is replaced by the Talwar robust regression function. Convexity, regulariz...

In traditional lucky imaging (TLI), many consecutive images of the same scene are taken with a high frame-rate camera, and all but the sharpest images are discarded before constructing the final shift-and-add image. Here we present an alternative image analysis pipeline -- The Thresher -- for these kinds of data, based on online multi-frame blind deconvolution. It makes use of all available data to obtain a best estimate of the astronomical scene in the context of reasonable ...