Related papers: Reconstruction of Gray-scale Images
Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In this paper, we analyze the recovery…
In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem. A class of algorithms reconstruct sensitivity encoded images of the coils first…
When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…
In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…
We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the…
One representation of possible errors in a grayscale image reconstruction is as another grayscale image estimating potentially worrisome differences between the reconstruction and the actual "ground-truth" reality. Visualizations and…
X-ray computed tomography (CT) reveals the materials' internal structures non-destructively from a tilt series of projected images. Filtered back projection (FBP) is a widely-adopted reconstruction algorithm in CT owing to its small…
Aiming at the problems of color distortion, blur and excessive noise of underwater image, an underwater image enhancement algorithm based on structure-texture reconstruction is proposed. Firstly, the color equalization of the degraded image…
The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. The posterior surface of the modes is convex in the linear regime, leading to a unique…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…
We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey…
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each…
We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
Removing noise from images is a challenging and fundamental problem in the field of computer vision. Images captured by modern cameras are inevitably degraded by noise which limits the accuracy of any quantitative measurements on those…