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Satellite-based Synthetic Aperture Radar (SAR) images can be used as a source of remote sensed imagery regardless of cloud cover and day-night cycle. However, the speckle noise and varying image acquisition conditions pose a challenge for…
Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) images. Many different schemes have been proposed for the restoration of intensity SAR images. Among the different possible approaches, methods based on…
In this paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge…
Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…
Noise is one of the primary sources of interference in seismic exploration. Many authors have proposed various methods to remove noise from seismic data; however, in the face of strong noise conditions, satisfactory results are often not…
Diffusion models have demonstrated remarkable potential in generating high-quality images. However, their tendency to replicate training data raises serious privacy concerns, particularly when the training datasets contain sensitive or…
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
Synthetic Aperture Radar (SAR) images are inherently corrupted by speckle noise, limiting their utility in high-precision applications. While deep learning methods have shown promise in SAR despeckling, most methods employ a single unified…
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the…
Although the advances of self-supervised blind denoising are significantly superior to conventional approaches without clean supervision in synthetic noise scenarios, it shows poor quality in real-world images due to spatially correlated…
Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the…
Current self-supervised denoising methods for paired noisy images typically involve mapping one noisy image through the network to the other noisy image. However, after measuring the spectral bias of such methods using our proposed Image…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
We present two versatile methods to generally enhance self-supervised monocular depth estimation (MDE) models. The high generalizability of our methods is achieved by solving the fundamental and ubiquitous problems in photometric loss…
This article aims to investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we…
Snapshot mosaic multispectral imagery acquires an undersampled data cube by acquiring a single spectral measurement per spatial pixel. Sensors which acquire $p$ frequencies, therefore, suffer from severe $1/p$ undersampling of the full data…
Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the…