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

Poisson noise suppression is an important preprocessing step in several applications, such as medical imaging, microscopy, and astronomical imaging. In this work, we propose a novel patch-wise Poisson noise removal strategy, in which the MMSE estimator is utilized in order to produce the denoising result for each image patch. Fast and accurate computation of the MMSE estimator is carried out using k-d tree search followed by search in the K-nearest neighbor graph. Our experim...

In this paper, we address the problem of denoising images degraded by Poisson noise. We propose a new patch-based approach based on best linear prediction to estimate the underlying clean image. A simplified prediction formula is derived for Poisson observations, which requires the covariance matrix of the underlying clean patch. We use the assumption that similar patches in a neighborhood share the same covariance matrix, and we use off-the-shelf Poisson denoising methods in...

This paper attempts to undertake the study of Restored Gaussian Blurred Images. by using four types of techniques of deblurring image as Wiener filter, Regularized filter, Lucy Richardson deconvlutin algorithm and Blind deconvlution algorithm with an information of the Point Spread Function (PSF) corrupted blurred image with Different values of Size and Alfa and then corrupted by Gaussian noise. The same is applied to the remote sensing image and they are compared with one an...

The Rayleigh limit and low Signal-to-Noise Ratio (SNR) scenarios pose significant limitations to optical imaging systems used in remote sensing, infrared thermal imaging, and space domain awareness. In this study, we introduce a Stochastic Sub-Rayleigh Imaging (SSRI) algorithm to localize point objects and estimate their positions, brightnesses, and number in low SNR conditions, even below the Rayleigh limit. Our algorithm adopts a maximum likelihood approach and exploits the...

We present a new method for joint likelihood deconvolution (Jolideco) of a set of astronomical observations of the same sky region in the presence of Poisson noise. The observations may be obtained from different instruments with different resolution, and different point spread functions. Jolideco reconstructs a single flux image by optimizing the posterior distribution based on the joint Poisson likelihood of all observations under a patch-based image prior. The patch prior ...

Images taken under the low-light condition often contain blur and saturated pixels at the same time. Deblurring images with saturated pixels is quite challenging. Because of the limited dynamic range, the saturated pixels are usually clipped in the imaging process and thus cannot be modeled by the linear blur model. Previous methods use manually designed smooth functions to approximate the clipping procedure. Their deblurring processes often require empirically defined parame...

I present a family of algorithms to reduce noise in astrophysical im- ages and image sequences, preserving more information from the original data than is retained by conventional techniques. The family uses locally adaptive filters ("noise gates") in the Fourier domain, to separate coherent image structure from background noise based on the statistics of local neighborhoods in the image. Processing of solar data limited by simple shot noise or by additive noise reveals image...

We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms. Our approach not only allows for the anti-aliasing of the images but also enables PSF deconvolution, resulting in enhanced restoration of extended sources, the highest PSNR, and reduced ringing artefacts. To test our method, we conducted numerical simulations that replicated observation runs of the CSST/VST tele...

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this study we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To...

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex optimization formulation with a cost function consisting of the sum of a likelihood function and a regularization function which the nuclear norm of the matrix. Instead of solving the optimization problem directly by semi-definite program (S...