Nonuniform sampling
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Using Deep Neural Networks to Reconstruct Non-uniformly Sampled NMR Spectra Open
Non-uniform and sparse sampling of multi-dimensional NMR spectra has over the last decade become an important tool to allow for fast acquisition of multi-dimensional NMR spectra with high resolution. The success of non-uniform sampling NMR…
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Gaussian Regularized Periodic Nonuniform Sampling Series Open
The periodic nonuniform sampling plays an important role in digital signal processing and other engineering fields. In this paper, we introduce the Gaussian regularization method to accelerate the convergence rate of periodic nonuniform sa…
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Inhomogeneous Poisson Sampling of Finite-Energy Signals With Uncertainties in Open
Spatiotemporal signal reconstruction from samples randomly gathered in a multidimensional space with uncertainty is a crucial problem for a variety of applications. Such a problem generalizes the reconstruction of a deterministic signal an…
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Nyquist Sampling and Degrees of Freedom of Electromagnetic Fields Open
A signal space approach is presented to study the Nyquist sampling, degrees of freedom and reconstruction of electromagnetic fields under non-line-of-sight conditions. Conventional signal processing tools, such as the multidimensional samp…
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Improving the sensitivity of FT-NMR spectroscopy by apodization weighted sampling Open
Apodization weighted acquisition is a simple approach to enhance the sensitivity of multidimensional NMR spectra by scaling the number of scans during acquisition of the indirect dimension(s). The signal content of the resulting spectra is…
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Tensor Completion From Regular Sub-Nyquist Samples Open
Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the maxi…
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Extreme Nonuniform Sampling for Protein NMR Dynamics Studies in Minimal Time Open
NMR spectroscopy is an extraordinarily rich source of quantitative dynamics of proteins in solution using spin relaxation or chemical exchange saturation transfer (CEST) experiments. However, 15N-CEST measurements require prolonged multidi…
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Orthogonal Full-Field Optical Sampling Open
Sampling is the first step to convert analogue into digital signals and one of the \nbasic concepts for information handling. All practical sampling systems, however, are accompanied \nwith errors. Bandwidth-limited signals can be seen as …
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NUScon: a community-driven platform for quantitative evaluation of nonuniform sampling in NMR Open
Although the concepts of nonuniform sampling (NUS) and non-Fourier spectral reconstruction in multidimensional NMR began to emerge 4 decades ago (Bodenhausen and Ernst, 1981; Barna and Laue, 1987), it is only relatively recently tha…
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Non‐Uniform and Absolute Minimal Sampling for High‐Throughput Multidimensional NMR Applications Open
Many biomolecular NMR applications can benefit from the faster acquisition of multidimensional NMR data with high resolution and their automated analysis and interpretation. In recent years, a number of non‐uniform sampling (NUS) approache…
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Non-Uniform Sampling in NMR Spectroscopy and the Preservation of Spectral Knowledge in the Time and Frequency Domains Open
The increased sensitivity under weighted non-uniform sampling (NUS) is demonstrated and quantified using Monte Carlo simulations of nuclear magnetic resonance (NMR) time- and frequency-domain signals. The concept of spectral knowledge is i…
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Demystifying Compressive Sensing [Lecture Notes] Open
The conventional Nyquist-Shannon sampling theorem has been fundamental to the acquisition of signals for decades, relating a uniform sampling rate to the bandwidth of a signal. However, many signals can be compressed after sampling, implyi…
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Non‐uniform sampling for NOESY? A case study on spiramycin Open
To date, most nuclear magnetic resonance (NMR)‐based 3‐D structure determinations of both small molecules and of biopolymers utilize the nuclear Overhauser effect (NOE) via NOESY spectra. The acquisition of high‐quality NOESY spectra is a …
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Compressed <span>NMR</span>: Combining compressive sampling and pure shift <span>NMR</span> techniques Open
Historically, the resolution of multidimensional nuclear magnetic resonance (NMR) has been orders of magnitude lower than the intrinsic resolution that NMR spectrometers are capable of producing. The slowness of Nyquist sampling as well as…
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Sampling and Reconstruction of Sparse Signals in Shift-Invariant Spaces: Generalized Shannon’s Theorem Meets Compressive Sensing Open
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, a…
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A Sampling Rate Selecting Algorithm for the Arbitrary Waveform Generator Open
The arbitrary waveform generator is now commonly used to generate waveforms in many fields. The Nyquist sampling theorem only provides an open interval for the sampling rate selection, but how to determine a specific sampling rate within t…
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Ergodic sampling: Acquisition design to maximize information from limited samples Open
Data acquisition using equal spacing has been a standard practice in geophysics. The dense uniform sampling derived from Nyquist–Shannon sampling includes redundant samples, and it is sufficient but not necessary to adequately record targe…
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Nonuniform Sampling Rate Conversion:An Efficient Approach Open
We present a discrete-time algorithm for nonuniform sampling rate conversion\nthat presents low computational complexity and memory requirements. It\ngeneralizes arbitrary sampling rate conversion by accommodating time-varying\nconversion …
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Delta-Ramp Encoder for Amplitude Sampling and Its Interpretation as Time Encoding Open
The theoretical basis for conventional acquisition of bandlimited signals\ntypically relies on uniform time sampling and assumes infinite-precision\namplitude values. In this paper, we explore signal representation and recovery\nbased on u…
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Signal reconstruction with generalized sampling Open
This paper studies the problem of reconstructing continuous-time signals from discrete-time uniformly sampled data. This signal reconstruction problem has been studied by the authors in various contexts, and led to a new signal processing …
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Unlimited Sampling From Theory to Practice: Fourier-Prony Recovery and Prototype ADC Open
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware im…
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AgileSAR: Achieving Wide-Swath Spaceborne SAR Based on Time-Space Sampling Open
High resolution and wide swath, which are related to imaging quality and observation efficiency, are the key specifications for spaceborne synthetic aperture radar (SAR). Owing to the restrictions of the Nyquist sampling theorem, it is dif…
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Filtering Property of Signal Sampling in General and Under-Sampling as a Specific Operation of Filtering Connected with Signal Shaping at the Same Time Open
In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when the Nyquist frequency is larger or equal to the maximal frequency in the spectrum of a signal sampled. We demo…
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Revisiting aliasing noise to build more robust sparsity in nonuniform sampling 2D‐NMR Open
A continuing priority is to better understand and resolve the barriers to using nonuniform sampling (NUS) in challenging small molecule 2D NMR with subsampling of the Nyquist grid (a.k.a. coverage) below 50%. Possible causes for artifacts,…
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Fundamental Distortion Limits of Analog-to-Digital Compression Open
Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bit…
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Centralized and Decentralized Data-Sampling Principles for Outer-Synchronization of Fractional-Order Neural Networks Open
This paper aims to investigate the outer-synchronization of fractional-order neural networks. Using centralized and decentralized data-sampling principles and the theory of fractional differential equations, sufficient criteria about outer…
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Analog-to-Information Conversion for Nonstationary Signals Open
In this paper, we consider the problem of analog-to-information conversion for nonstationary signals, which exhibit time-varying properties with respect to spectral contents. Nowadays, sampling for nonstationary signals is mainly based on …
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Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN Open
The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a descriptio…
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Non‐uniform sampling to enhance the performance of compact NMR for characterizing new psychoactive substances Open
Efficient and robust analytical methods are needed to improve the identification and subsequent regulation of new psychoactive substances (NPS). NMR spectroscopy is a unique method able to determine the structure of small molecules such as…
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A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition--Part I: Range, Resolution, and Universal Convergence States Open
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear sy…