JOSR-Net: A jointly optimized sampling and reconstruction deep learning network for accelerated NMR spectroscopy

This paper presents an ultra-low-power non-uniform sampling scheme using a derivative-based algorithm that can maintain a comparable accuracy to other non-uniform sampling schemes but with less complexity and lower power consumption. In this method, the change in the derivative of the signal above certain threshold values is used to identify high signal activity for retention of the significant points of the signal. The scheme is implemented using simple building blocks that calculate and compare the change in approximate real-time derivative to a tunable threshed value that can be adjusted to obtain the desired Compression Factor (CF) and Post-Reconstruction Signal-to-Noise plus Distortion Ratio (PR-SNDR) for different signal types. Fabricated in TSMC's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.13 \mu \text{m}$ </tex-math></inline-formula> CMOS technology and tested with real-world biomedical signals, the proposed Derivative Dependent Sampling (DDS) system consumes a maximum power of 155 nW while achieving a CF of more than 6 for an Electrocardiography (ECG) signal. By adding the proposed DDS block to a data acquisition and processing system, the non-uniform sampling can reduce the power dissipation of the entire system.

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some n JCC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

A unified approach to the representation and processing of a class of images which are not bandlimited but belong to the space of locally bandlimited signals is presented. A nonuniform sampling theorem (Clark et al, 1985) for functions belonging to this space is extended, and a class of nonstationary stochastic processes is considered. The space of locally bandlimited signals is shown to be a reproducing-kernel space. A generalized projection theorem can therefore be applied, yielding either a continuous or a discrete projection filter. The former can be used for image conditioning prior to nonuniform sampling, while the latter provides a general tool for image representation by nonuniform sampling schemes. The problem of finding the local bandwidth of a given signal, in order to generate an optimal sampling scheme, is addressed in the context of signal representation in the combined position-frequency space. The stochastic estimation of parameters which characterize the local bandwidth is discussed. Bounds on the error resulting from the utilization of nonexact position-varying signal parameters are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A nonuniform sampling scheme is described for measuring the mutual intensity of the wave field produced in a plane a distance z from a spatially incoherent, three-dimensional source object. Both uniform and nonuniform sampling are analyzed and discussed in detail, and comparisons of the two schemes are made. It is shown that nonuniform sampling requires fewer measurements than uniform sampling to specify the coherence function. Additionally, the smallest separation required between measurement points is larger for the nonuniform case.

Dealing with visualizations containing large data set is a challenging issue and, in the field of information visualization, almost every visual technique reveals its drawback when visualizing large number of items. To deal with this problem we introduce a formal environment, modeling in a virtual space the image features we are interested in (e.g, absolute and relative density, clusters, etc.) and we define some metrics able to characterize the image decay. Such metrics drive our automatic techniques (i.e., not uniform sampling) rescuing the image features and making them visible to the user. In This work we focus on 2D scatter-plots, devising a novel non uniform data sampling strategy able to preserve in an effective way relative densities.

The accuracy of measurement-driven mobile coverage maps depends on the quality, density and pattern of the signal strength observations. Thus, identifying an efficient measurement data collection methodology is essential, especially when considering the cost associated with the measurement collection approaches (e.g., drive tests, crowd approaches). We propose ZipWeave, a novel measurement data collection and fusion framework for building efficient and reliable measurement-based mobile coverage maps. ZipWeave incorporates a novel nonuniform sampling strategy to achieve reliable coverage maps with reduced sample size. Assuming prior knowledge of the propagation characteristics of the region of interest, we first examine the potential gains of this non-uniform sampling strategy in different cases via a measurement-based statistical analysis methodology; this involves irregular spatial tessellation of the region of interest into sub-regions with internally similar radio propagation characteristics and sampling based on these sub-regions. We then present a practical form of ZipWeave nonuniform sampling strategy that can be used even without any prior information. In all our evaluations, we show that the ZipWeave non-uniform sampling approach reduces the samples by half compared to the common systematic-random sampling, while maintaining similar accuracy. Moreover, we show that the other key feature of ZipWeave to combine high-quality controlled measurements (that present limited geographic footprint similar to drive tests) with crowdsourced measurements (that cover a wider footprint) leads to more reliable mobile coverage maps overall.

We consider the problem of reconstructing a 2D bandlimited signal from its nonuniform samples taken in polar coordinates. We introduce two nonuniform sampling strategies in polar coordinates and develop algorithms for reconstructing the signal from these samples. The proposed methods collect nonuniform samples along concentric circles or radial lines, where the circles or lines are nonuniformly distributed. We then apply these methods to the problem of reconstruction of tomographic images and show through simulations that they result in a higher quality of reconstruction with respect to the traditionally used algorithms.

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

We present a strategy for stereospecific NMR assignment of Hβ2 and Hβ3 protons in mid-size proteins (~150 residues). For such proteins, resonance overlap in standard experiments is severe, thereby preventing unambiguous assignment of a large fraction of β-methylenes. To alleviate this limitation, assignment experiments may be run in high static fields, where higher decoupling power is required. Three-bond Hα–Hβ J-couplings (3JHα–Hβ) are critical for stereospecific assignments of β-methylene protons, and for determining rotameric χ1 states. Therefore, we modified a pulse sequence designed to measure accurate 3JHα–Hβ couplings such that probe heating was reduced, while the decoupling performance was improved. To further increase the resolution, we applied non-uniform sampling (NUS) schemes in the indirect 1H and 13C dimensions. The approach was applied to two medium-sized proteins, odorant binding protein 22 (OBP22; 14.4 kDa) and Pin1 (18.2 kDa), at 900 MHz polarizing fields. The coupling values obtained from NUS and linear sampling were extremely well correlated. However, NUS decreased the overlap of Hβ2/3 protons, thus supplying a higher yield of extracted 3JHα-Hβ coupling values when compared with linear sampling. A similar effect could be achieved with linear prediction applied to the linearly sampled data prior to the Fourier transformation. Finally, we used 3JHα–Hβ couplings from Pin1 in combination with either conventional or exact nuclear Overhauser enhancement (eNOE) restraints to determine the stereospecific assignments of β-methylene protons. The use of eNOEs further increased the fraction of unambiguously assigned resonances when compared with procedures using conventional NOEs.

A new approach to the representation and reconstruction of non-bandlimited signals using non-uniform sampling schemes is introduced. The proposed method is based on estimation of a time distortion transformation, under which the original signal becomes bandlimited, and can thus be reconstructed. This method is optimal in the sense that it requires the minimal sampling rate for exact reconstruction of the signal. The estimation is iterative, and can be used with most available techniques of localized bandwidth approximation. The resultant time transformation can be considered also as a new means for the definition of local bandwidth.

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling locations as well as the optimal presampling filter to minimize the reconstruction distortion. We first show that to achieve the optimal distortion, no presampling filter is necessary for any arbitrary sampling rate. Then, we provide a complete characterization of optimal distortion for low and high sampling rates (with respect to the signal bandwidth). We also provide bounds on the reconstruction distortion for rates in the intermediate region. It is shown that nonuniform sampling outperforms uniform sampling for low sampling rates. In addition, the optimal nonuniform sampling set is robust with respect to missing sampling values. On the other hand, for the sampling rates above the Nyquist rate, the uniform sampling strategy is optimal.

Robust and transferable quantification of NMR spectral quality using IROC analysis

The concept of frequency transfer function plays a fundamental role in characterizing a linear digital signal processor's dynamical behavior. Invariably, the input number sequence to be operated upon is assumed to have originated through the process of uniformly sampling a continuous-time signal. It is then only natural that most studies related to a linear digital signal processor's transfer function are based upon the uniform sampling model. In a variety of very important applications, however, the number sequence to be pro cessed is generated by a nonuniform sampling scheme. For example, in radar signal processing, stagger sampling is often used in order to reduce the effects of the Sampled Signals so-called "blind velocity"phenomenon (e.g., see refs.