Related papers: Compressive Deconvolution in Random Mask Imaging
We study sparse spikes deconvolution over the space of Radon measures on $\mathbb{R}$ or $\mathbb{T}$ when the input measure is a finite sum of positive Dirac masses using the BLASSO convex program. We focus on the recovery properties of…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolution and reconstruction under non-smooth convex regularization.…
Measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields including optical communications,…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…
Image inpainting has earned substantial progress, owing to the encoder-and-decoder pipeline, which is benefited from the Convolutional Neural Networks (CNNs) with convolutional downsampling to inpaint the masked regions semantically from…
The non-uniform sampling is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partial sampled exponentials is highly expected in general signal processing and…
Decoding visual stimuli from brain recordings aims to deepen our understanding of the human visual system and build a solid foundation for bridging human and computer vision through the Brain-Computer Interface. However, reconstructing…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recover the deblurred image. The problem is of strong practical relevance since many imaging devices…
This paper considers the blind deconvolution of multiple modulated signals, and an arbitrary filter. Multiple inputs $\boldsymbol{s}_1, \boldsymbol{s}_2, \ldots, \boldsymbol{s}_N =: [\boldsymbol{s}_n]$ are modulated (pointwise multiplied)…
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…
We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution $\mu$, from a binned Poisson convolution model. This question is motivated, among others, by super-resolution laser microscopy…
The most ubiquitous form of computational aberration correction for microscopy is deconvolution. However, deconvolution relies on the assumption that the point spread function is the same across the entire field-of-view. This assumption is…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
Defocus blur is a physical consequence of the optical sensors used in most cameras. Although it can be used as a photographic style, it is commonly viewed as an image degradation modeled as the convolution of a sharp image with a…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of…