10 accepted papers
This paper aims to provide a new perspective on understanding the resolution limit by examining a recently proposed spectrum estimator based on the Christoffel-Darboux Kernel. Different from other estimators, this estimator possesses a definite criterion of resolvability building on the well known S…
Sparse support recovery from multiple measurement vectors is studied in this paper. Instead of using any relaxations, we impose the explicit ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -norm constraint and propose to identify the joint spa…
Separation-aware super resolution algorithms are studied in this paper. Motivated by the optics applications, we consider the mixture model of Airy disks, and propose to develop general mapping operators that can enforce a specific separation constraint. The proposed operators can work with existing…
This paper studies the problem of discrete super-resolution. Existing stability guarantees rely on the fact that certain separation conditions are satisfied by the true support. However, such structural conditions have not been exploited in the corresponding algorithmic designs. This paper proposes…
This paper studies the overfitting in discrete super-resolution problem. In particular, we solve for the estimate that simply overfits the noisy measurements. By doing this, we no longer require the prior knowledge of additive noise to set the parameter of sparse reconstruction algorithm to ensure t…
This paper considers the problem of lower bounding the mean-squared-error (MSE) of unbiased super-resolution estimates. In literature, only upper bounds on the MSE are available which scale with the so-called super-resolution factor (SRF). However, the upper bound does not indicate whether the MSE i…
This paper considers the problem of super-resolution reconstruction by casting it as an optimization problem with positive constraints and non-convex objective function. Enforcing the solution to be simultaneously sparse and non-negative naturally leads to a non-convex l <sub xmlns:mml="http://www.w…
This paper considers the problem of super-resolution with positive constraints. By utilizing the concept of Modulus of Continuity (MC), we propose a unified framework for analyzing the robustness of super-resolution reconstruction in presence of noise, which is algorithm-independent and emphasizes t…
This paper considers the problem of co-array interpolation for direction-of-arrival (DOA) estimation with sparse nonuniform arrays. By utilizing the much longer difference co-array associated with these arrays, it is possible to perform DOA estimation of more sources than sensors. Since the co-array…
The problem of sparse phase retrieval is considered where the goal is to recover a sparse complex valued vector (with s non zero elements) from the magnitudes of its linear measurements. Using a modified and partially randomized version of a newly proposed structured sampler, namely the Partial Nest…