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Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion…
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least $4.1~\mathrm{dB}$ across this range. We achieve sub-single-photon precision…
Light detection and ranging systems reconstruct scene depth from time-of-flight measurements. For low light-level depth imaging applications, such as remote sensing and robot vision, these systems use single-photon detectors that resolve…
We consider the two-dimensional multi-target detection (MTD) problem of estimating a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. The MTD model serves as a…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
It is a crucial issue to realize real-time piston correction in the area of sparse aperture imaging. This paper introduces an optical diffractive neural network-based piston sensing method, which can achieve light-speed sensing. By using…
We present a new modelling approach for longitudinal count data that is motivated by the increasing availability of longitudinal RNA-sequencing experiments. The distribution of RNA-seq counts typically exhibits overdispersion,…
This study aims to improve photon counting CT (PCCT) image resolution using denoising diffusion probabilistic models (DDPM). Although DDPMs have shown superior performance when applied to various computer vision tasks, their effectiveness…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
In the field of medical image analysis, deep learning models have demonstrated remarkable success in enhancing diagnostic accuracy and efficiency. However, the reliability of these models is heavily dependent on the quality of training…
The negative binomial model, which generalizes the Poisson distribution model, can be found in applications involving low-photon signal recovery, including medical imaging. Recent studies have explored several regularization terms for the…
Computer vision techniques play a central role in the perception stack of autonomous vehicles. Such methods are employed to perceive the vehicle surroundings given sensor data. 3D LiDAR sensors are commonly used to collect sparse 3D point…
We propose a new approach called LiDAR-Flow to robustly estimate a dense scene flow by fusing a sparse LiDAR with stereo images. We take the advantage of the high accuracy of LiDAR to resolve the lack of information in some regions of…
In recent years, advances in high throughput sequencing technology have led to a need for specialized methods for the analysis of digital gene expression data. While gene expression data measured on a microarray take on continuous values…