Related papers: Compressive Fourier Transform Spectroscopy
Single-shot ultrafast absorbance spectroscopy based on the frequency encoding of the kinetics is analyzed theoretically and implemented experimentally. The kinetics are sampled in the frequency domain using linearly chirped, amplified 33 fs…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
Schlieren deflectometry aims at characterizing the deflections undergone by refracted incident light rays at any surface point of a transparent object. For smooth surfaces, each surface location is actually associated with a sparse…
Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time $\sigma_{B} \propto 1/T$ (Heisenberg scaling)…
Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
Single-shot ultrafast spectroscopy based on the frequency encoding of transient absorbance kinetics (FDSS) is demonstrated. These kinetics are sampled spectrally using linearly chirped pulses derived from a Ti:sapphire laser. A variable…
In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is…
Terahertz microscopy has attracted attention owing to distinctive characteristics of the THz frequency region, particularly non-ionizing photon energy, spectral fingerprint, and transparency to most nonpolar materials. Nevertheless, the…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Nano-FTIR imaging is a powerful scanning-based technique at nanometer spatial resolution which combines Fourier transform infrared spectroscopy (FTIR) and scattering-type scanning near-field optical microscopy (s-SNOM). However, recording…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the…
Compressive sensing has been used to demonstrate scene reconstruction and source localization in a wide variety of devices. To date, optical compressive sensors have not been able to achieve significant volume reduction relative to…
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
Optical frequency-comb-based-high-resolution spectrometers offer enormous potential for spectroscopic applications. Although various implementations have been demonstrated, the lack of suitable mid-infrared comb sources has impeded…
Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). Recently, a spread spectrum compressed sensing MRI method modulates an image with a quadratic phase. It performs better than…