Related papers: Leveraging Diversity and Sparsity in Blind Deconvo…
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…
This paper addresses the estimation of signals with sublinear sparsity sent over the additive white Gaussian noise channel. This fundamental problem arises in designing denoisers used in message-passing algorithms for sublinear sparsity.…
Hyperspectral images (HSIs) play a crucial role in remote sensing but are often degraded by complex noise patterns. Ensuring the physical property of the denoised HSIs is vital for robust HSI denoising, giving the rise of deep…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However,…
For an undirected/directed hypergraph $G=(V,E)$, its Laplacian $L_G\colon\mathbb{R}^V\to \mathbb{R}^V$ is defined such that its ``quadratic form'' $\boldsymbol{x}^\top L_G(\boldsymbol{x})$ captures the cut information of $G$. In particular,…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
This paper concerns solving the sparse deconvolution and demixing problem using $\ell_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and…
We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach.…
We consider the problem of estimating an unknown matrix $\boldsymbol{X}\in {\mathbb R}^{m\times n}$, from observations $\boldsymbol{Y} = \boldsymbol{X}+\boldsymbol{W}$ where $\boldsymbol{W}$ is a noise matrix with independent and…
We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where…
This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…
The Phase Diverse Speckle (PDS) problem is formulated mathematically as Multi Frame Blind Deconvolution (MFBD) together with a set of Linear Equality Constraints (LECs) on the wavefront expansion parameters. This MFBD-LEC formulation is…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
Diversity is a powerful means to increase the transmission performance of wireless communications. For the case of fountain codes relaying, it has been shown previously that introducing diversity is also beneficial since it counteracts…
This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm,…
Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…
In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed…
The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and…