Related papers: Regularized Richardson-Lucy Algorithm for Sparse R…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
Crucial information barely visible to the human eye is often embedded in a series of low-resolution images taken of the same scene. Super-resolution enables the extraction of this information by reconstructing a single image, at a high…
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…
The problem of Poisson denoising appears in various imaging applications, such as low-light photography, medical imaging and microscopy. In cases of high SNR, several transformations exist so as to convert the Poisson noise into an additive…
The observations in many applications consist of counts of discrete events, such as photons hitting a dector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model.…
This paper proposes a deep learning architecture that attains statistically significant improvements over traditional algorithms in Poisson image denoising espically when the noise is strong. Poisson noise commonly occurs in low-light and…
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…
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…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
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…
Image enhancement approaches often assume that the noise is signal independent, and approximate the degradation model as zero-mean additive Gaussian. However, this assumption does not hold for biomedical imaging systems where sensor-based…
We have developed an image restoration technique based on the Richardson-Lucy algorithm optimized for GLAST-LAT image analysis. Our algorithm is original since it utilizes the PSF (point spread function) that is calculated for each event.…
This paper studies the problem of exact localization of sparse (point or extended) objects with noisy data. The crux of the proposed approach consists of random illumination. Several recovery methods are analyzed: the Lasso, BPDN and the…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
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…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…