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

Large-scale astronomical surveys can capture numerous images of celestial objects, including galaxies and nebulae. Analysing and processing these images can reveal intricate internal structures of these objects, allowing researchers to conduct comprehensive studies on their morphology, evolution, and physical properties. However, varying noise levels and point spread functions can hamper the accuracy and efficiency of information extraction from these images. To mitigate thes...

Richardson-Lucy (RL) deconvolution is one of the classical methods widely used in X-ray astronomy and other areas. Amid recent progress in image processing, RL deconvolution still leaves much room for improvement under a realistic situations. One direction is to include the positional dependence of a point-spread function (PSF), so-called RL deconvolution with a spatially variant PSF (RL$_{\rm{sv}}$). Another is the method of estimating a reliable number of iterations and the...

We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to treat in a theo- retical analysis. In our formulation, we interpret the observation through the Poisson noise channel as a likelihood, and evaluate the bound of it with a Gaussian function using a latent variable method. We then introduce a...

This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based restoration algorithms to account for the observed image being corrupted by mixed Poisson-Gaussian noise and quantization errors.

Photon-limited images are often seen in fields such as medical imaging. Although the number of collected photons on an image sensor statistically follows Poisson distribution, this type of noise is intractable, unlike Gaussian noise. In this study, we propose a Bayesian restoration method of Poisson corrupted image using Integrated Nested Laplace Approximation (INLA), which is a computational method to evaluate marginalized posterior distributions of latent Gaussian models (L...

Since time immemorial, noise has been a constant source of disturbance to the various entities known to mankind. Noise models of different kinds have been developed to study noise in more detailed fashion over the years. Image processing, particularly, has extensively implemented several algorithms to reduce noise in photographs and pictorial documents to alleviate the effect of noise. Images with sparse colours-lesser number of distinct colours in them-are common nowadays, e...

In the past years modern mathematical methods for image analysis have led to a revolution in many fields, from computer vision to scientific imaging. However, some recently developed image processing techniques successfully exploited by other sectors have been rarely, if ever, experimented on astronomical observations. We present here tests of two classes of variational image enhancement techniques: "structure-texture decomposition" and "super-resolution" showing that they ar...

Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence, denoising a Poisson-corrupted image while preserving important details can be challenging. In this paper, we propose a Poisson denoising model by incorporating the weighted anisotropic-isotropic total variation (AITV) as a regularization. ...

We study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. To analyze its performance, we formulate the oversampled binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We show that, with a single-photon quantization threshold and large oversampling factors, the Cram\'er-Rao lower bound (CRLB...

Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the entire images. However, if the PSF is modeled as a sum of orthogonal functions that are individually constant in form over the images, but whose relative amplitudes encode the PSF spatial variability, then separation of variables again allo...