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This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be a standard problem in inverse theory. Such and similar problems routinely arise in numerous areas of applied sciences, including optical…
We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…
Image blurring refers to the degradation of an image wherein the image's overall sharpness decreases. Image blurring is caused by several factors. Additionally, during the image acquisition process, noise may get added to the image. Such a…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
Motion blurry images challenge many computer vision algorithms, e.g, feature detection, motion estimation, or object recognition. Deep convolutional neural networks are state-of-the-art for image deblurring. However, obtaining training data…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Noise reduction techniques based on deep learning have demonstrated impressive performance in enhancing the overall quality of recorded speech. While these approaches are highly performant, their application in audio engineering can be…
We consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two…
We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the…
Image deblurring is an essential image preprocessing technique, aiming to recover clear and detailed images form blurry ones. However, existing algorithms often fail to effectively integrate multi-scale feature extraction with frequency…
Ptychography is an attractive advance of coherent diffraction imaging (CDI), which can provide high lateral resolution and wide field of view. The theoretical resolution of ptychography is dose-limited, therefore making ptychography…
Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…
This paper addresses the deconvolution of an image that has been obtained by superimposing many copies of an underlying unknown image of interest. The superposition is assumed to not be exact due to noise, and is described using an error…
We consider a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this \textit{dual-blind deconvolution} (DBD) problem, a common receiver…
Patient scans from MRI often suffer from noise, which hampers the diagnostic capability of such images. As a method to mitigate such artifact, denoising is largely studied both within the medical imaging community and beyond the community…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Blind image deblurring is a fundamental and challenging computer vision problem, which aims to recover both the blur kernel and the latent sharp image from only a blurry observation. Despite the superiority of deep learning methods in image…
Blind signal separation (BSS) is an important and challenging signal processing task. Given an observed signal which is a superposition of a collection of unknown (hidden/latent) signals, BSS aims at recovering the separate, underlying…
We study the recovery of the distribution function $F_X$ of a random variable $X$ that is subject to an independent additive random error $\varepsilon$. To be precise, it is assumed that the target variable $X$ is available only in the form…