Related papers: A Theory of Computational Resolution Limit for Lin…
Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the…
The aim of two-dimensional line spectral estimation is to super-resolve the spectral point sources of the signal from time samples. In many associated applications such as radar and sonar, due to cut-off and saturation regions in electronic…
The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. An important figure of merit for sensing time dependent signals is the spectral…
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…
The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are…
In the paper, we consider the line spectral estimation problem in an unlimited sensing framework (USF), where a modulo analog-to-digital converter (ADC) is employed to fold the input signal back into a bounded interval before quantization.…
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…
Quantum fluctuations yield inevitable noises in quantum detection. We derive an upper bound of signal to noise ratio for arbitrary quantum detection described by trace-class operators with discrete spectra. The bound is independent of…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes…
For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises…
Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem is to reconstruct the source number, positions, and amplitudes. This problem arises from many important applications in…