Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals

Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics

Optical measurements often exhibit mixed Poisson-Gaussian noise statistics, which hampers image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using maximum-likelihood estimation, we devise a practical method to account for camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment.Comment: Contains main and supplementary document

A variational approach to denoising problem

A digital image can be created by different digital devices, such as digital cameras, X-ray scanners, etc. In practice, such devices can give unexpected defects, for example, noise. The Gaussian noise and Poisson noise are very important, but their combination is important too. This mixed noise usually appears in electronic microscopic images, in aerospace images, etc. Our goal is to combine ROF model (for Gaussian noise removal) and modified ROF model (for Poisson noise removal) to create new model that can treat this combination effectively. Our model will treat this combination with considering proportion of noise between them.

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

Period Estimation and Noise in a Neutrally Stable Stochastic Oscillator

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems

Optimally Stabilized PET Image Denoising Using Trilateral Filtering

Low-resolution and signal-dependent noise distribution in positron emission tomography (PET) images makes denoising process an inevitable step prior to qualitative and quantitative image analysis tasks. Conventional PET denoising methods either over-smooth small-sized structures due to resolution limitation or make incorrect assumptions about the noise characteristics. Therefore, clinically important quantitative information may be corrupted. To address these challenges, we introduced a novel approach to remove signal-dependent noise in the PET images where the noise distribution was considered as Poisson-Gaussian mixed. Meanwhile, the generalized Anscombe's transformation (GAT) was used to stabilize varying nature of the PET noise. Other than noise stabilization, it is also desirable for the noise removal filter to preserve the boundaries of the structures while smoothing the noisy regions. Indeed, it is important to avoid significant loss of quantitative information such as standard uptake value (SUV)-based metrics as well as metabolic lesion volume. To satisfy all these properties, we extended bilateral filtering method into trilateral filtering through multiscaling and optimal Gaussianization process. The proposed method was tested on more than 50 PET-CT images from various patients having different cancers and achieved the superior performance compared to the widely used denoising techniques in the literature.Comment: 8 pages, 3 figures; to appear in the Lecture Notes in Computer Science (MICCAI 2014

Iterative Poisson-Gaussian Noise Parametric Estimation for Blind Image Denoising

International audienceThis paper deals with noise parameter estimation from a single im- age under Poisson-Gaussian noise statistics. The problem is formu- lated within a mixed discrete-continuous optimization framework. The proposed approach jointly estimates the signal of interest and the noise parameters. This is achieved by introducing an adjustable reg- ularization term inside an optimized criterion, together with a data fidelity error measure. The optimal solution is sought iteratively by alternating the minimization of a label field and of a noise param- eter vector. Noise parameters are updated at each iteration using an Expectation-Maximization approach. The proposed algorithm is inspired from a spatial regularization approach for vector quantiza- tion. We illustrate the usefulness of our approach on macroconfocal images. The identified noise parameters are applied to a denoising algorithm, so yielding a fully automatic denoising scheme