Related papers: Mathematical Foundation of Sparsity-based Multi-sn…
We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used…
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable…
Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and…
Received signal strength (RSS) based source localization method is popular due to its simplicity and low cost. However, this method is highly dependent on the propagation model which is not easy to be captured in practice. Moreover, most…
Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…
An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved…
Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are…
In large-scale spatial surveys, such as the forthcoming ESA Euclid mission, images may be undersampled due to the optical sensors sizes. Therefore, one may consider using a super-resolution (SR) method to recover aliased frequencies, prior…
This paper studies stable recovery of a collection of point sources from its noisy $M+1$ low-frequency Fourier coefficients. We focus on the super-resolution regime where the minimum separation of the point sources is below $1/M$. We…
In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…
We address the challenging problem of estimating the directions-of-arrival (DOAs) of multiple off-grid signals using a single snapshot of one-bit quantized measurements. Conventional DOA estimation methods face difficulties in tackling this…
Rydberg-based Direction-of-Arrival (DoA) estimation has been hampered by the complexity of receiver arrays and the single-target, narrow-band limitations of existing single-receiver methods. This paper introduces a novel approach that…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing…
Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
A priori information on the positivity of source intensities is ubiquitous in imaging fields and is also important for a multitude of super-resolution and deconvolution algorithms. However, the fundamental resolution limit of positive…
Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
Direction of Arrival (DOA) estimation of multiple narrow-band coherent or partially coherent sources is a major challenge in array signal processing. Though many subspace- based algorithms are available in literature, none of them tackle…