اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBenchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization
143
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in order to discover when and how each method can be used most profitably. We find that filter diagonalization provides the best results for Lorentzian signals, while compressed sensing and super-resolution perform better for arbitrary signals.
قيم البحث
اقرأ أيضاً
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly b
eneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing, and analyze its typical performance using statistical mechanics. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the L1-norm minimization approach, asymptotically saturating the performance obtained when the non-zero entries positions of the signal are known. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.
Image registration is the inference of transformations relating noisy and distorted images. It is fundamental in computer vision, experimental physics, and medical imaging. Many algorithms and analyses exist for inferring shift, rotation, and nonline
ar transformations between image coordinates. Even in the simplest case of translation, however, all known algorithms are biased and none have achieved the precision limit of the Cramer Rao bound (CRB). Following Bayesian inference, we prove that the standard method of shifting one image to match another cannot reach the CRB. We show that the bias can be cured and the CRB reached if, instead, we use Super Registration: learning an optimal model for the underlying image and shifting that to match the data. Our theory shows that coarse-graining oversampled images can improve registration precision of the standard method. For oversampled data, our method does not yield striking improvements as measured by eye. In these cases, however, we show our new registration method can lead to dramatic improvements in extractable information, for example, inferring $10times$ more precise particle positions.
Neutron direct-geometry time-of-flight chopper spectroscopy is instrumental in studying fundamental excitations of vibrational and/or magnetic origin. We report here that techniques in super-resolution optical imagery (which is in real-space) can be
adapted to enhance resolution and reduce noise for a neutron spectroscopy (an instrument for mapping excitations in reciprocal space). The procedure to reconstruct super-resolution energy spectra of phonon density of states relies on a realization of multi-frame registration, accurate determination of the energy-dependent point spread function, asymmetric nature of instrument resolution broadening, and iterative reconstructions. Applying these methods to phonon density of states data for a graphite sample demonstrates contrast enhancement, noise reduction, and ~5-fold improvement over nominal energy resolution. The data were collected at three different incident energies measured at the Wide Angular-Range Chopper Spectrometer at the Spallation Neutron Source.
Two dimensional (2D) peak finding is a common practice in data analysis for physics experiments, which is typically achieved by computing the local derivatives. However, this method is inherently unstable when the local landscape is complicated, or t
he signal-to-noise ratio of the data is low. In this work, we propose a new method in which the peak tracking task is formalized as an inverse problem, thus can be solved with a convolutional neural network (CNN). In addition, we show that the underlying physics principle of the experiments can be used to generate the training data. By generalizing the trained neural network on real experimental data, we show that the CNN method can achieve comparable or better results than traditional derivative based methods. This approach can be further generalized in different physics experiments when the physical process is known.
Despite of their success, the results of first-principles quantum mechanical calculations contain inherent numerical errors caused by various approximations. We propose here a neural-network algorithm to greatly reduce these inherent errors. As a dem
onstration, this combined quantum mechanical calculation and neural-network correction approach is applied to the evaluation of standard heat of formation $DelH$ and standard Gibbs energy of formation $DelG$ for 180 organic molecules at 298 K. A dramatic reduction of numerical errors is clearly shown with systematic deviations being eliminated. For examples, the root--mean--square deviation of the calculated $DelH$ ($DelG$) for the 180 molecules is reduced from 21.4 (22.3) kcal$cdotp$mol$^{-1}$ to 3.1 (3.3) kcal$cdotp$mol$^{-1}$ for B3LYP/6-311+G({it d,p}) and from 12.0 (12.9) kcal$cdotp$mol$^{-1}$ to 3.3 (3.4) kcal$cdotp$mol$^{-1}$ for B3LYP/6-311+G(3{it df},2{it p}) before and after the neural-network correction.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
