Related papers: Utilizing the Wavelet Transform's Structure in Com…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
While diffusion-based generative models have made significant strides in visual content creation, conventional approaches face computational challenges, especially for high-resolution images, as they denoise the entire image from noisy…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
We propose a compressed sampling and dictionary learning framework for fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is generated from a model for the reflected sensor signal. Imperfect prior knowledge is…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
Learning from limited data is challenging because data scarcity leads to a poor generalization of the trained model. A classical global pooled representation will probably lose useful local information. Many few-shot learning methods have…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the…
Image deblurring is a challenging problem in imaging due to its highly ill-posed nature. Deep learning models have shown great success in tackling this problem but the quest for the best image quality has brought their computational…
Compressed sensing (CS) using overcomplete wavelet dictionaries has been a well-investigated topic in the recent times for image and vision applications. In this paper, different overcomplete wavelet transforms have been studied to estimate…
Image restoration aims to enhance low quality images, producing high quality images that exhibit natural visual characteristics and fine semantic attributes. Recently, the diffusion model has emerged as a powerful technique for image…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the…
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…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…