Signal-to-noise Ratio Of Spectra Research Articles

In vivo brain MRS at a 1.5T clinical scanner: Optimized derivative fast Fourier transform for high-resolution spectra from time signals encoded with and without water suppression

We study single-voxel in vivo proton magnetic resonance spectroscopy (MRS) of white matter in the brain of a 25 year old healthy male volunteer. The free induction decay (FID) data of short length (0.5KB) are encoded at a long echo time (272 ms) with and without water suppression at a clinical scanner of a weak magnetic field (1.5T). For these FIDs, the fast Fourier transform (FFT) gives sparse, rough and metabolically uninformative spectra. In such spectra, resolution and signal to noise ratio (SNR) are poor. Exponential or Gaussian filters applied to the FIDs can improve SNR in the FFT spectra, but only at the expense of the worsened resolution. This impacts adversely on in vivo MRS for which both resolution and SNR of spectra need to be very good or excellent, without necessarily resorting to stronger magnetic fields. Such a long sought goal is at last within reach by means of the optimized derivative fast Fourier transform (dFFT), which dramatically outperforms the FFT in every facet of signal estimations. The optimized dFFT simultaneously improves resolution and SNR in derivative spectra. They are presently shown to be of comparably high quality irrespective of whether water is suppressed or not in the course of FID encodings. The ensuing benefits of utmost relevance in the clinic include a substantial shortening of the patient examination time. The implied significantly better cost-effectiveness should make in vivo MRS at low-field clinical scanners (1.5T) more affordable to ever larger circles of hospitals worldwide.

Denoising magnetic resonance spectroscopy (MRS) data using stacked autoencoder for improving signal-to-noise ratio and speed of MRS.

While magnetic resonance imaging (MRI) provides high resolution anatomical images with sharp soft tissue contrast, magnetic resonance spectroscopy (MRS) enables non-invasive detection and measurement of biochemicals and metabolites. However, MRS has low signal-to-noise ratio (SNR) when concentrations of metabolites are in the range of millimolar. Standard approach of using a high number of signal averaging (NSA) to achieve sufficient SNR comes at the cost of a long acquisition time. We propose to use deep-learning approaches to denoise MRS data without increasing NSA. This method has potential to reduce the acquisition time as well as improve SNR and quality of spectra, which could enhance the diagnostic value and broaden the clinical applications of MRS. The study was conducted using data collected from the brain spectroscopy phantom and human subjects. We utilized a stack auto-encoder (SAE) network to train deep learning models for denoising low NSA data (NSA=1, 2, 4, 8, and 16) randomly truncated from high SNR data collected with high NSA (NSA=192), which were also used to obtain the ground truth. We applied both self-supervised and fully-supervised training approaches and compared their performance of denoising low NSA data based on improvement in SNR. To prevent overfitting, the SAE network was trained in a patch-based manner. We then tested the denoising methods on noise-containing data collected from the phantom and human subjects, including data from brain tumor patients. We evaluated their performance by comparing the SNR levels and mean squared errors (MSEs) calculated for the whole spectra against high SNR "ground truth", as well as the value of chemical shift of N-acetyl-aspartate (NAA) before and after denoising. With the SAE model, the SNR of low NSA data (NSA=1) obtained from the phantom increased by 28.5% and the MSE decreased by 42.9%. For low NSA data of the human parietal and temporal lobes, the SNR increased by 32.9% and the MSE decreased by 63.1%. In all cases, the chemical shift of NAA in the denoised spectra closely matched with the high SNR spectra without significant distortion to the spectra after denoising. Furthermore, the denoising performance of the SAE model was more effective in denoising spectra with higher noise levels. The reported SAE denoising method is a model-free approach to enhance the SNR of MRS data collected with low NSA. With the denoising capability, it is possible to acquire MRS data with a few NSA, shortening the scan time while maintaining adequate spectroscopic information for detecting and quantifying the metabolites of interest. This approach has the potential to improve the efficiency and effectiveness of clinical MRS data acquisition by reducing the scan time and increasing the quality of spectroscopic data.

232. Implementation of an edited-PRESS sequence for the detection of the 2-Hydroxyglutarate metabolite

Purpose The 2-Hydroxyglutarate (2-HG) metabolite can be quantified with MR-spectroscopy using an edited-PRESS sequence with shifted echo times. This metabolite has a key role in staging low-grade gliomas. The aim of this work was to implement the edited-PRESS for the detection of the 2-HG within our MR-scanner. Furthermore, we studied several sequence parameters in order to optimize the spectrum signal-to-noise-ratio (SNR), while limiting the acquisition time. Methods A homemade phantom containing a solution of choline (2 mM) and creatine (6 mM) was built to simulate the healthy brain tissue. A Philips Ingenia-3T scanner was used in service-mode to generate single-voxel MR-spectra using the edited-PRESS. The dependence of the SNR with the number of signal acquisitions (NSA) and the voxel volume was characterized. Furthermore, the impact of two shimming algorithms (automatic and semi-automatic) was studied. The LCModel software was used to fit the acquired spectra. The root-mean-square (RMS) between measured and fitted spectra was employed to evaluate the fit quality. Results The SNR showed a linear correlation (R2 = 0.99) with the quantity [NSÂ(1/2) × Voxel Volume], which is consistent with the theoretical behaviour. In terms of spectrum SNR, a not significant difference (p = 0.38, paired t-test) was found between the shimming algorithms (Fig. 1). The fit RMS was inversely proportional (R2 = 0.99) to the quantity [NSÂ(1/2) × Voxel Volume]. A simple formula was derived from these results in order to calculate the optimum NSA, once the voxel volume has been fixed. Conclusions The implemented PRESS generated MR-spectra whose SNR dependence was compatible with the theoretical behavior. Since the semi-automatic shimming algorithm did not improve the spectrum SNR significantly, the automatic modality is suggested. The developed formula can be used by the MR-technologists to rapidly determine the optimum NSA of the edited-PRESS, once the voxel volume has been fixed ( Table 1 ).

Hybridized robust chemometrics approach for direct rapid determination of trace biometals in tissue utilizing energy dispersive X-ray fluorescence and scattering (EDXRFS) spectrometry

Direct rapid energy dispersive X-ray fluorescence and scattering (EDXRFS) analysis of trace biometals in soft body tissues is important because it has an immense potential for biomedical applications. Unfortunately this is challenging because soft body tissues are characterized by dark matrix problems, weak analyte fluorescence, scattering, poor signal-to-noise ratio (SNR) of the analyte and spectral overlaps due to the properties of the detector and detection process. We report on hybridized utility of robust chemometrics approach for spectral preprocessing towards improving the quality of spectra towards quantitative analysis of trace biometals in soft body tissue. The study was based on (5–20 µm thick) paraffin wax model ‘standards’ spiked with biometals Fe, Cu, Mn, Zn, Co, Na and Mg. Wavelet transform (WT) and principal component analysis (PCA) were used conjointly for de-noising and mathematical enhancement of resolution. There was improved SNR of spectra by a factor of 3 compared to use of WT alone. The preprocessed spectra were used as input to artificial neural network (ANN) and partial least squares (PLS) models for developing multivariate calibration strategies for quantitative analysis. Both models predicted the concentrations of the biometals better than when raw spectra were utilized (R2 ~ 0.892–0.954 before, and ~ 0.990–0.998 after preprocessing for ANNs; and R2 ~ 0.876–0.931 before, and ~ 0.977–0.992 after preprocessing for PLS). There was also improvement in prediction of Na and Mg in model tissue when both fluorescence and scatter were utilized conjointly (EDXRFS) i.e. R2 = 0.970 for fluorescence alone and R2 = 0.998 for both fluorescence and scatter for Na; and R2 = 0.934 for fluorescence alone and R2 = 0.993 for both fluorescence and scatter for Mg for ANN model. The accuracy of the calibration model was tested using Oyster tissue (NIST 1566b). The results of all analyzed elements were in agreement with certified values to ≤ 6%. This shows proof-of-concept for use of hybridized robust chemometrics approaches for direct rapid determination of trace biometals in soft tissue utilizing EDXRFS spectrometry; an approach that has potential for biomedical applications of EDXRF.

Accuracy study for lock‐in amplifiers in a scanning near‐infrared spectrometer

When a lock-in amplifier was employed in a scanning near-infrared spectrometer, there was the problem of low signal-to-noise ratio (SNR) of spectra. This study investigates the impact of unstable measured signal frequency in the lock-in amplifier. The analysis concludes that when the frequency of the measured signal and reference signal are not equal due to frequency fluctuations, the amplitude detection results are inaccurate and change periodically with the initial phase of the measured signal. According to analysis results, a zero-phase detection method is designed in the spectrometer, where the measured signal phase is judged to guarantee detection starting at the zero-phase position. The experimental results indicate that the average of the SNR of spectra is 2376 using the zero-phase detection method, which is approximately three times that of the original system and coincides with the results of the theoretical calculation (2273) and simulation analysis (2234).

Characterizing the Degrading Effects of Scattering by Atmospheric Fog on the Spatial Resolution of Imaging Systems

In this paper the effects of scattering, with four atmospheric fog aerosols models, on the overall point spread function (PSF) of an imaging system are investigated. The PSF and radiometric calculations are then used to estimate the mean numbers of direct path and scattered photons detected by the imaging system in the visible and near infra-red (NIR) spectral bands of the electro-magnetic spectrum (EMS), for a horizontal near-ground imaging scenario. The image spectrum signal-to-noise ratio (SNR) is then used to estimate the noise effective spatial resolution of the imaging system which emphasizes the degrading effect of fog aerosol models on the spatial resolution of the imaging systems.

Estimating the image spectrum signal-to-noise ratio for imaging through scattering media

The image spectrum signal-to-noise ratio (SNR) provides a means of estimating the noise effective spatial resolution of an imaging system and a means of estimating the highest spatial frequency which can be reconstructed with a postdetection image reconstruction algorithm. Previous work has addressed the effects of aerosol scattering on the overall point spread function (PSF). Here, we seek to extend these results to also account for the effects of measurement noise and to then estimate the noise effective resolution of the system, which accounts for scattering effects on the PSF and measurement noise in the detector. We use a previously published approach to estimating the effective PSF and radiometric calculations to estimate the mean numbers of direct and scattered photons detected by an imaging system due to reflected radiation in the visible and near-infrared, and emitted radiation in mid-infrared (MIR) band, for a horizontal near-ground imaging scenario. The analysis of the image spectrum SNR presented here shows a reduction in the value of noise effective cutoff spatial frequency for images taken through fog aerosol media, and hence emphasizes the degrading effect of fog aerosol models on the spatial resolution of imaging systems.

Use of signal to noise ratio and area change rate of spectra to evaluate the Visible/NIR spectral system for fruit internal quality detection

The stability of a spectroscopic measuring system is very important in non-destructive internal quality measurement of agriculture products by Visible and NIR (Vis/NIR) spectroscopy at factory level. However, few works have been published about how to evaluate whether or not the spectroscopic measuring system is reasonable. In this paper, signal to noise ratio (SNR) and area change rate (ACR) of the spectra of reference standard were used to evaluate the Vis/NIR spectral system. Two different systems with different light sources (LS1 and LS2) were considered. The results showed that the SNR recorded at each selected wavelength in the condition of LS1 was higher than that recorded in the condition of LS2, and the ACR between 550nm and 920nm in the condition of LS1 was smaller than that of LS2. Meanwhile, in the verification experiment by calibration and cross-validation analysis using fruits, the results obtained in the condition of LS1 were all better than that of LS2, and the best results were correlation coefficient of calibration (rc)=0.948, root mean square error of calibration (RMSEC)=0.299°Brix, correlation coefficient of cross-validation (rcv)=0.924, and root mean square error of cross-validation (RMSECV)=0.359°Brix. This was well matched to the results of SNR and ACR analysis. This study demonstrates that SNR and ACR of spectra can be used to evaluate the reasonable of the Vis/NIR spectral measuring system.

Exploring signal-to-noise ratio and sensitivity in non-uniformly sampled multi-dimensional NMR spectra

It is well established that non-uniform sampling (NUS) allows acquisition of multi-dimensional NMR spectra at a resolution that cannot be obtained with traditional uniform acquisition through the indirect dimensions. However, the impact of NUS on the signal-to-noise ratio (SNR) and sensitivity are less well documented. SNR and sensitivity are essential aspects of NMR experiments as they define the quality and extent of data that can be obtained. This is particularly important for spectroscopy with low concentration samples of biological macromolecules. There are different ways of defining the SNR depending on how to measure the noise, and the distinction between SNR and sensitivity is often not clear. While there are defined procedures for measuring sensitivity with high concentration NMR standards, such as sucrose, there is no clear or generally accepted definition of sensitivity when comparing different acquisition and processing methods for spectra of biological macromolecules with many weak signals close to the level of noise. Here we propose tools for estimating the SNR and sensitivity of NUS spectra with respect to sampling schedule and reconstruction method. We compare uniformly acquired spectra with NUS spectra obtained in the same total measuring time. The time saving obtained when only 1/k of the Nyquist grid points are sampled is used to measure k-fold more scans per increment. We show that judiciously chosen NUS schedules together with suitable reconstruction methods can yield a significant increase of the SNR within the same total measurement time. Furthermore, we propose to define the sensitivity as the probability to detect weak peaks and show that time-equivalent NUS can considerably increase this detection sensitivity. The sensitivity gain increases with the number of NUS indirect dimensions. Thus, well-chosen NUS schedules and reconstruction methods can significantly increase the information content of multidimensional NMR spectra of challenging biological macromolecules.

Denoising of time-resolved PIV for accurate measurement of turbulence spectra and reduced error in derivatives

The accuracy of time-resolved PIV (TRPIV) turbulence measurements is limited by white noise, which reduces the signal-to-noise ratio (SNR) of small-scale velocity fluctuations. This paper demonstrates a novel energy filter that extends the concept of spectral noise subtraction to the time domain. The filter is equivalent to the spectral subtraction of white noise energy, and therefore it can recover the true signal energy. Its effectiveness is evaluated by comparing two-component (2C) TRPIV and constant temperature anemometry (CTA) measurements performed in grid-generated turbulence (Re λ = 90). The denoised PIV measurements exhibit a SNR equivalent to those of a high-performance CTA system. The temporal spectra of velocity fluctuations and derivatives are accurately recovered, with an improvement in dynamic range by a factor of $$\fancyscript{O}(10^3)$$ . The error in dissipation estimates derived from the frequency spectrum is reduced to approximately 2 %. The correlation coefficient between spatial gradients computed directly and those computed via Taylor’s hypothesis improves from 0.83 to 0.95. The mean-square error reduction is found to be equivalent in the frequency and wavenumber domains, although we observe that frequency domain filtering has a limited ability to improve the SNR of spatial spectra at high wavenumbers. The performance of the energy filter is shown to be sensitive to the convergence of the measured spectra; therefore, we provide sampling criteria to ensure optimal implementation in measurements of turbulent flows.

Broadband spectroscopy of dynamic impedances with short chirp pulses

An impedance spectrum of dynamic systems is time dependent. Fast impedance changes take place, for example, in high throughput microfluidic devices and in operating cardiovascular systems. Measurements must be as short as possible to avoid significant impedance changes during the spectrum analysis, and as long as possible for enlarging the excitation energy and obtaining a better signal-to-noise ratio (SNR). The authors propose to use specific short chirp pulses for excitation. Thanks to the specific properties of the chirp function, it is possible to meet the needs for a spectrum bandwidth, measurement time and SNR so that the most accurate impedance spectrogram can be obtained. The chirp wave excitation can include thousands of cycles when the impedance changes slowly, but in the case of very high speed changes it can be shorter than a single cycle, preserving the same excitation bandwidth. For example, a 100 kHz bandwidth can be covered by the chirp pulse with durations from 10 µs to 1 s; only its excitation energy differs also 105 times. After discussing theoretical short chirp properties in detail, the authors show how to generate short chirps in the microsecond range with a bandwidth up to a few MHz by using digital synthesis architectures developed inside a low-cost standard field programmable gate array.

Incoherent DOA Estimation in Uniform Antenna Arrays with Inordinate Spacing Using a Subband Hopping Approach

Given a certain transmission frequency, the Shannon spatial sampling limit defines an upper bound for the antenna element spacing. Beyond this bound, the exceeded ambiguity avoids correct estimation of the signal parameters (i.e., array manifold crossing). In this survey, the problem of simultaneous signal and direction-of-arrival (DOA) estimation of broadband sources is addressed when the element spacing of a uniform array antenna (uniform linear array (ULA)) is inordinate. It is illustrated that one can resolve the aliasing ambiguity by utilizing the inherent frequency diversity of the broadband sources. An algorithm based on maximum likelihood estimation (MLE) has been developed to estimate the transmitted data signal and the DOA of each source. Through confirmatory simulation, it is shown that the performance gain of the proposed setup is potentially significant, specifically under a low signal-to-noise ratio (SNR) and when the transmitters are closely spaced. This relaxes the stringent maximum element-spacing constraint of ULAs pertinent to the upper-bound frequency of transmission and suggests that the element spacing—which in practical applications results in detrimental element coupling—can be conveniently increased, in particular under wide transmission spectrum and low SNR (e.g., license-free communication). A method similar to the frequency hopping approach (i.e., subband hopping) is utilized for the problem of source associations and identification. In the sequel, a suboptimal subspace-based algorithm is proposed and its performance is investigated. An approximate expression for the estimation error has also been developed to gauge the behavior of the proposed setup.

An investigation of filter choice for filtered back-projection reconstruction in PET

A key parameter in the practical application of filtered back-projection (FBP), the standard clinical image reconstruction algorithm for positron emission tomography (PET), is the choice of a low-pass filter window function and its cut-off frequency. However, the filter windows and cut-off frequencies for clinical reconstruction are usually chosen empirically, based on a small sample of images and filters. By considering the features of the signal and noise spectra in a sinogram, the desired image resolution, and the signal-to-noise ratio (SNR) of the filtered sinogram, a methodology for informed selection of a filter function and cut-off frequency for FBP was investigated. Simulations of sinogram data similar to whole body or cardiac studies provided information on the signal and noise frequency-domain spectra of noisy projection data. The improvements in SNR with different filter windows and cut-off frequencies were evaluated and compared. The projection spectrum SNR measure did not prove to be an accurate indicator of subjective image quality or lesion detectability with variations in Poisson noise and image resolution.

Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images

Adaptive optics systems have been used to compensate for the degrading effects of atmospheric turbulence in images collected with large astronomical telescopes. Postdetection processing techniques are also employed to further improve adaptive optics compensated images. Typically, many short-exposure images are collected, recentered to compensate for tilt, and then averaged to overcome randomness in the images and improve signal-to-noise ratio (SNR). Experience shows that some short-exposure images in a data set are better than others. The frame selection postdetection processing technique uses an image quality metric to discard low-quality frames and improve image spectrum SNR. We address key issues pertaining to frame selection performance limits. Noise trade-offs are used to investigate minimum object brightness for successful application of the frame selection technique. Limits imposed by noise effects result in a minimum object brightness of apparent visual magnitude +8 for point sources and +4 for a +2-m length representative extended object imaged with a 1-m-diam telescope with no central obscuration. Effective average point spread functions for the point source and the representative extended object after frame selection processing under equivalent seeing conditions are almost identical. Thus, deconvolution could be applied to these images obtained via frame selection.

Calibration of Airborne Visible/Infrared Imaging Spectrometer Data (AVIRIS) to reflectance and mineral mapping in hydrothermal alteration zones: An example from the “Cuprite mining district”

Abstract High‐spectral resolution images (AVIRIS) over the Cuprite mining area have been used to evaluate atmospheric calibration algorithms and test several mineral mapping techniques. Four normalization techniques have been applied: (1) the Flat‐Field Method, (2) the Equal Area normalization technique using the Internal Average Reflectance (IAR) Spectrum, (3) the Empirical Line Method, and (4) the Atmospheric Absorption Removal Method (ATREM) which uses a standard empirical atmosphere model. The algorithms have been evaluated in terms of their ability to remove both solar irradiance and atmospheric absorption features, noise, artifacts, and spectral interpretability. Signal‐to‐noise ratio (SNR) has been calculated as the ratio of the mean of the digital number (DN) values (reflectivity)) and the standard deviation of the DN values (noise) for pixel spectra. An empirical relation was found between SNR and number of pixel spectra averaged. Spectral interpretability was evaluated by using the difference spectrum (e.g. laboratory spectrum minus pixel spectrum) for areas with known occurrences of clay minerals. These difference spectra were useful in evaluating the removal of atmospheric features. Mineral mapping was done using (1) a comparison between pixel spectra and laboratory spectra, (2) colour‐composites with bands selected on shoulders and centres of expected absorption features, (3) colour coded spectra, and (4) an indicator kriging techniqure which uses bands on the shoulders and centre of expected absorption features to derive the probability that a pixel belongs to a certain mineral class.

Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing

The use of predetection compensation for the effects of atmospheric turbulence combined with postdetection image processing for imaging applications with large telescopes is addressed. Full and partial predetection compensation with adaptive optics is implemented by varying the number of actuators in the deformable mirror. The theoretical expression for the single-frame power spectrum signal-to-noise ratio (SNR) is reevaluated for the compensated case to include the statistics of the compensated optical transfer function. Critical to this analysis is the observation that the compensated optical transfer function does not behave as a circularly complex Gaussian random variable except at high spatial frequencies. Results from a parametric study of performance are presented to demonstrate improvements in power spectrum estimation for both point sources and an extended object and improvements in the Fourier phase spectrum estimation for an extended object. Full compensation is shown to provide a large improvement in the power spectrum SNR over the uncompensated case, while successively smaller amounts of predetection compensation provide smaller improvements, until a low degree of compensation gives results essentially identical to those of the uncompensated case. Three regions of performance were found with respect to the object Fourier phase spectrum estimate obtained from bispectrum postprocessing: (1) the fully compensated case in which bispectrum postprocessing provides no improvement in the phase estimate over that obtained from a fully compensated long-exposure image, (2) a partially compensated regime in which applying bispectrum postprocessing to the compensated images provides a phase spectrum estimation superior to that of the uncompensated bispectrum case, and (3) a poorly compensated regime in which the results are essentially indistinguishable from those of the uncompensated case. Accurate simulations were used to obtain some parameters for the power spectrum SNR analysis and to obtain the Fourier phase spectrum results.