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We introduce a new multiscale restoration algorithm for images with few photons counts and its use for denoising XMM data. We use a thresholding of the wavelet space so as to remove the noise contribution at each scale while preserving the…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
Microscopy is a powerful visualization tool in biology, enabling the study of cells, tissues, and the fundamental biological processes; yet, the observed images typically suffer from blur and background noise. In this work, we propose a…
In this paper, we propose a new method for Salt-and-Pepper noise removal from images. Whereas most of the existing methods are based on Ordered Statistics filters, our method is based on the growing theory of Sparse Signal Processing. In…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
Image denoising is a classic restoration problem. Yet, current deep learning methods are subject to the problems of generalization and interpretability. To mitigate these problems, in this project, we present a framework that is capable of…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
The paper shows the potential of sparsity-based methods in restoring quantized signals. Following up on the study of Brauer et al. (IEEE ICASSP 2016), we significantly extend the range of the evaluation scenarios: we introduce the analysis…
Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
The motivation of this paper is to introduce a novel framework for the restoration of images corrupted by mixed Gaussian-impulse noise. To this aim, first, an adaptive curvelet thresholding criterion is proposed which tries to adaptively…
Supervised Gaussian denoisers exhibit limited generalization when confronted with out-of-distribution noise, due to the diverse distributional characteristics of different noise types. To bridge this gap, we propose a histogram matching…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
Photoacoustic tomography is a hybrid biomedical technology, which combines the advantages of acoustic and optical imaging. However, for the conventional image reconstruction method, the image quality is affected obviously by artifacts under…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
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…
We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…
An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…