Related papers: A Provably Convergent Scheme for Compressive Sensi…

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…

In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of…

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent…

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

In oversampled adaptive sensing (OAS), noisy measurements are collected in multiple subframes. The sensing basis in each subframe is adapted according to some posterior information exploited from previous measurements. The framework is…

Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…

This paper proposes a novel approach to regularize the \textit{ill-posed} and \textit{non-linear} blind image deconvolution (blind deblurring) using deep generative networks as priors. We employ two separate generative models --- one…

Deep image denoising networks have achieved impressive success with the help of a considerably large number of synthetic train datasets. However, real-world denoising is a still challenging problem due to the dissimilarity between…

Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse…

The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier…

In recent years, Generative Adversarial Networks (GANs) have shown substantial progress in modeling complex distributions of data. These networks have received tremendous attention since they can generate implicit probabilistic models that…

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…