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DOE OSTI2026

Spectral deconvolution without the deconvolution: Extracting temperature from x-ray Thomson scattering spectra without the source-and-instrument function

X-ray Thomson scattering (XRTS) probes the dynamic structure factor of the system, but the measured spectrum is broadened by the combined source-and-instrument function (SIF) of the setup. In order to extract properties such as temperature from an XRTS spectrum, the broadening by the SIF needs to be removed. Recent work [Dornheim et al. Nat. Commun. 13 , 7911 (2022)] has suggested that the SIF may be deconvolved using the two-sided Laplace transform. However, the extracted information can depend strongly on the shape of the input SIF, and the SIF is in practice challenging to measure accurately. Here, we propose an alternative approach: we demonstrate that considering ratios of Laplace-transformed XRTS spectra collected at different scattering angles is equivalent to performing the deconvolution, but without the need for explicit knowledge of the SIF. From these ratios, it is possible to directly extract the temperature from the scattering spectra, when the system is in thermal equilibrium. We find the method to be generally robust to spectral noise and physical differences between the spectrometers, and we explore situations in which the method breaks down. Furthermore, the fact that consistent temperatures can be extracted for systems in thermal equilibrium indicates that non-equilibrium effects could be identified by inconsistent temperatures of a few eV between the ratios of three or more scattering angles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2016

Wavenumber-frequency deconvolution of aeroacoustic microphone phased array data of arbitrary coherence

Deconvolution of aeroacoustic data acquired with microphone phased arrays is a computationally-challenging task for distributed sources with arbitrary coherence. A new technique for performing such deconvolution is proposed. This technique relies on analysis of the array data in the wavenumber-frequency domain, allowing for fast convolution and reduced storage requirements when compared to traditional coherent deconvolution. A positive semidefinite constraint for the iterative deconvolution procedure is implemented and shows improved behavior in terms of quantifiable convergence metrics when compared to a standalone covariance inequality constraint. A series of simulations validates the method's ability to resolve coherence and phase angle relationships between partially-coherent sources, as well as determines convergence criteria for deconvolution analysis. Simulations for point sources near the microphone phased array show potential for handling such data in the wavenumber-frequency domain. In particular, a physics-based integration boundary calculation is described, and can successfully isolate sources and track the appropriate integration bounds with and without the presence of flow. Magnitude and phase relationships between multiple sources are successfully extracted. Limitations of the deconvolution technique are determined from the simulations, particularly in the context of a simulated acoustic field in a closed test section wind tunnel with strong boundary layer contamination. A final application to a trailing edge noise experiment conducted in an open-jet wind tunnel matches best estimates of acoustic levels from traditional calculation methods and qualitatively assesses the coherence characteristics of the trailing edge noise source.

phased array↗

NASA NTRS1993

What do you gain from deconvolution? - Observing faint galaxies with the Hubble Space Telescope Wide Field Camera

We describe experiments with deconvolutions of simulations of deep HST Wide Field Camera images containing faint, compact galaxies to determine under what circumstances there is a quantitative advantage to image deconvolution, and explore whether it is (1) helpful for distinguishing between stars and compact galaxies, or between spiral and elliptical galaxies, and whether it (2) improves the accuracy with which characteristic radii and integrated magnitudes may be determined. The Maximum Entropy and Richardson-Lucy deconvolution algorithms give the same results. For medium and low S/N images, deconvolution does not significantly improve our ability to distinguish between faint stars and compact galaxies, nor between spiral and elliptical galaxies. Measurements from both raw and deconvolved images are biased and must be corrected; it is easier to quantify and remove the biases for cases that have not been deconvolved. We find no benefit from deconvolution for measuring luminosity profiles, but these results are limited to low S/N images of very compact (often undersampled) galaxies.

Schade, David J.↗

NASA NTRS1984

Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution

Mass spectrometer data in the form of ion current versus mass-to-charge ratio often include overlapping mass peaks, especially in low- and medium-resolution instruments. Numerical deconvolution of such data effectively enhances the resolution by decreasing the overlap of mass peaks. In this paper two approaches to deconvolution are presented: a function-domain iterative technique and a Fourier transform method which uses transform-domain function-continuation. Both techniques include data smoothing to reduce the sensitivity of the deconvolution to noise. The efficacy of these methods is demonstrated through application to representative mass spectrometer data and the deconvolved results are discussed and compared to data obtained from a spectrometer with sufficient resolution to achieve separation of the mass peaks studied. A case for which the deconvolution is seriously affected by Gibbs oscillations is analyzed.

Ioup, J. W.↗

NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 3

The Always-Convergent Iterative Noise Removal and Deconvolution Method of Ioup is applied as a single-filter in the transform domain to deconvolution with both narrow and wide Gaussian impulse response functions. The wraparound error for both cases is also studied. A method is developed by which one can find the optimum iteration number for single-filter iterative deconvolution of sampled data. The method employs the mean square error (MSE), the square of the difference between the deconvolved result and the input, for optimization. The MSE decreases as the deconvolution iterations proceed, but at the optimum iteration number, the MSE starts to increase. This procedure is repeated for signal-to-noise ratio of 10 to 150. The optimum iteration number and the MSE are plotted vs SNR. By knowing the SNR for a particular experiment, one can find the optimum iteration number and MSE.

Ioup, George E.↗

DOE OSTI2024

Image Deconvolution and Point-spread Function Reconstruction with STARRED: A Wavelet-based Two-channel Method Optimized for Light-curve Extraction

We present starred, a point-spread function (PSF) reconstruction, two-channel deconvolution, and light-curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, starred performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a high-signal-to-noise-ratio, high-resolution frame combining all data and the photometry of all point sources in the field of view as a function of time. Of note, starred also provides exquisite PSF models for each data frame. We showcase three applications of starred in the context of the imminent LSST survey and of JWST imaging: (i) the extraction of supernovae light curves and the scene representation of their host galaxy; (ii) the extraction of lensed quasar light curves for time-delay cosmography; and (iii) the measurement of the spectral energy distribution of globular clusters in the "Sparkler," a galaxy at redshift z = 1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. starred is implemented in jax, leveraging automatic differentiation and graphics processing unit acceleration. This enables the rapid processing of large time-domain data sets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Deconvolution of dynamic heterogeneity in protein structure

Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1978

The application of a time-domain deconvolution technique for identification of experimental acoustic-emission signals

A method is presented for the signature analysis of pulses by reconstructing in the time domain the shape of the pulse prior to its passing through the measurement system. This deconvolution technique is first evaluated using an idealized system and analytical pulse models and is shown to provide improved results. An experimental situation is then treated; system-component models are developed for the digitizer, tape recorder, filter, transducer and mechanical structure. To accommodate both calibration results and manufacturer's data, and to provide stable mathematical models entails considerable effort: some 30 parameters must be identified to model this system - which is still a substantial approximation - albeit of very high order. Experimental pulses generated by a ball drop, spark discharge and a tearing crack are then deconvoluted 'back through' the system as modeled, using this technique. These results are compared and indicate (a) that consistent shapes may be expected from a given type of source and (b) that some sources can be identified with greater clarity using the deconvolution approach.

Houghton, J. R.↗

NASA NTRS1980

The direct deconvolution of X-ray spectra

The method of deconvolution of proportional counter X-ray spectra as outlined by Blissett and Cruise is reviewed with particular emphasis on low-energy spectra. This method involves the expansion of the incident spectrum in terms of a set of orthonormal singular functions which propagate independently through the detector matrix. When applied to low-energy detectors which typically exhibit absorption features in their efficiency curves, the initial Blissett and Cruise prescription is shown to be unstable. Alternative methods for handling the efficiency are described and evaluated. In the deconvolution of steep spectra, additional distortions are shown to arise as a result of sidelobe oscillations in the effective response functions. A selective weighting procedure is thus introduced to suppress spurious features of this type. Finally, the role of filtering in the deconvolution procedure is discussed and several suitable forms for the filter are suggested.

Kahn, S. M.↗

NASA NTRS1981

Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments

Mathematical deconvolution of digitized analog signals from scientific measuring instruments is shown to be a means of extracting important information which is otherwise hidden due to time-constant and other broadening or distortion effects caused by the experiment. Three different approaches to deconvolution and their subsequent application to recorded data from three analytical instruments are considered. To demonstrate the efficacy of deconvolution, the use of these approaches to solve the convolution integral for the gas chromatograph, magnetic mass spectrometer, and the time-of-flight mass spectrometer are described. Other possible applications of these types of numerical treatment of data to yield superior results from analog signals of the physical parameters normally measured in aerospace simulation facilities are suggested and briefly discussed.

Wood, G. M.↗

NASA NTRS1986

Optimal application of Morrison's iterative noise removal for deconvolution

Morrison's iterative method of noise removal can be applied for both noise removal alone and noise removal prior to deconvolution. This method is applied to noise of various noise levels added to determine the optimum use of the method. The phase shift method of migration and modeling is evaluated and the results are compared to Stolt's approach. A method is introduced by which the optimum iterative number for deconvolution can be found. Statistical computer simulation is used to describe the optimum use of two convergent iterative techniques for seismic data. The Always-Convergent deconvolution technique was applied to data recorded during the quantitative analysis of materials through NonDestructive Evaluation (NDE) in which ultrasonic signals were used to detect flaws in substances such as composites.

Ioup, George E.↗

NASA NTRS1987

Nimbus 7 earth radiation budget wide field of view climate data set improvement. I - The earth albedo from deconvolution of shortwave measurements

A deconvolution method for extracting the top of the atmosphere (TOA) mean, daily albedo field from a set of wide-FOV (WFOV) shortwave radiometer measurements is proposed. The method is based on constructing a synthetic measurement for each satellite observation. The albedo field is represented as a truncated series of spherical harmonic functions, and these linear equations are presented. Simulation studies were conducted to determine the sensitivity of the method. It is observed that a maximum of about 289 pieces of data can be extracted from a set of Nimbus 7 WFOV satellite measurements. The albedos derived using the deconvolution method are compared with albedos derived using the WFOV archival method; the developed albedo field achieved a 20 percent reduction in the global rms regional reflected flux density errors. The deconvolution method is applied to estimate the mean, daily average TOA albedo field for January 1983. A strong and extensive albedo maximum (0.42), which corresponds to the El Nino/Southern Oscillation event of 1982-1983, is detected over the south central Pacific Ocean.

Hucek, Richard R.↗

NASA NTRS1987

Optimal application of Morrison's iterative noise removal for deconvolution. Appendices

Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.

Ioup, George E.↗

NASA NTRS1989

Extracting ocean surface information from altimeter returns - The deconvolution method

An evaluation of the deconvolution method for estimating ocean surface parameters from ocean altimeter waveforms is presented. It is shown that this method presents a fast, accurate way of determining the ocean surface parameters from noisy altimeter data. Three parameters may be estimated by using this method, including the altimeter-height error, the ocean-surface standard deviation, and the ocean-surface skewness. By means of a Monte Carlo experiment, an 'optimum' deconvolution algorithm and the accuracies with which the above parameters may be estimated using this algorithm are determined. Then the influence of instrument effects, such as errors in calibration and pointing-angle estimation, on the estimated parameters is examined. Finally, the deconvolution algorithm is used to estimate height and ocean-surface parameters from Seasat data.

Rodriguez, Ernesto↗

NASA NTRS1991

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution

The final report for work on the determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution is presented. Papers and theses prepared during the research report period are included. Among all the research results reported, note should be made of the specific investigation of the determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution. A methodology was developed to determine design and operation parameters for error minimization when deconvolution is included in data analysis. An error surface is plotted versus the signal-to-noise ratio (SNR) and all parameters of interest. Instrumental characteristics will determine a curve in this space. The SNR and parameter values which give the projection from the curve to the surface, corresponding to the smallest value for the error, are the optimum values. These values are constrained by the curve and so will not necessarily correspond to an absolute minimum in the error surface.

Ioup, George E.↗

NASA NTRS2012

Wavespace-Based Coherent Deconvolution

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Bahr, Christopher J.↗

NASA NTRS2017

Mass Spectra Deconvolution of Gaseous Mixtures Containing Volatile Organic Compounds

The Spacecraft Atmosphere Monitor (S.A.M.) analyzes all gaseous pollutants in the 1-150Th mass-to-charge range based on their positive-ion mass spectra. Of particular interest is the Trace Gas Analysis (TGA) mode of operation in which S.A.M detects minute amounts of volatile organic compounds (VOC). Pollutant component of the ambient air is sampled on demand in twenty full mass spectra per second. All spectra is accumulated in two-second intervals by an on-board Field Programmable Gate Arrays (FPGA) unit. Mass spectra represents the number of detected fragment ions in a given mass-to-charge ratio channel. Electron impact ionization of neutral molecules results in creation of numerous fragment ions and most of organic compounds will contribute several identical fragments. Despite the presence of these molecular isobars, we developed the deconvolution algorithm capable of identifying target species based on their characteristic fragmentation patterns. We investigate the efficiency of deconvolution algorithm as a function of mass resolution with which mass spectrum is acquired. Higher the mass resolution, better the chances are to distinguish between stereoisomers using their fragmentation propensities, but also results in higher data volumes to be processed by a set of small footprint software stacks hosted by an on-board computer. Finding the balance between deconvolution accuracy and generated data volume under time constrains and limited computing resources is the main topic of this study.

Darrach, M.↗

NASA NTRSDate not supplied

Accounting for the Influence of Decorrelation in Microphone Phased Array Deconvolution Methods

Microphone phased arrays are a common tool for use in aeroacoustic wind tunnel testing. The analysis of acquired array data is known to suffer from decorrelation effects, where the coherence of an acoustic wave measured by a pair of microphones is degraded as the wave passes through a turbulent free shear layer or boundary layer. This paper describes, in detail, how to mitigate the influence of decorrelation effects when processing array data with deconvolution methods. This is done using the DAMAS algorithm as an example, applied to recent airframe noise test data acquired in the NASA Langley 14- by 22-Foot Subsonic Tunnel. Two ways of handling the turbulent propagation modeling, both assuming plane wave propagation, are described. Results show that while turbulence model fit parameters may differ, both methods output extremely similar deconvolution results. Further improvements likely require more accurate mean shear layer data prior to developing more involved turbulence models.

microphone array↗