Spectral Correction Algorithm Research Articles

Material classification using basis material decomposition from spectral X-ray CT

Spectral X-ray Computed Tomography (CT) exploits advanced photon counting detectors (PCD) to measure a material’s spectrally resolved linear attenuation coefficient (LAC) with the simultaneous spectral acquisition at multiple energy thresholds. We present a method for material classification using spectral CT. The method employs a basis material decomposition model and estimates the effective atomic number (Zeff) from the spectral LAC measurements. Basis material decomposition builds on the fact that the LAC of any material can be well approximated by a linear combination of LACs of basis materials, with known Zeff values at the extremes of the relevant Zeff range. Spectral distortions of the energy spectrum due to the physical interactions between photons and the multi-energy-bin PCD such as charge sharing and photon pileup are corrected by a spectral correction algorithm. The validation of the method has been performed with experimental data acquired with a custom laboratory instrument for spectral CT, examining “real life” phantoms with materials in the range of 6≤Zeff≤15. The classification performance is estimated for different numbers of projections, energy bins and basis materials in LAC decomposition. When using just 12 projections, 15 energy bins and two basis materials, the method gives a relative deviation of 2.2% for Zeff, while this deviation is 5.9% when spectral correction is not used. The classification method is now ready for use in security screening where modern spectral CT systems are employed.

Significance of the spectral correction of photon counting detector response in material classification from spectral x-ray CT.

Purpose: Photon counting imaging detectors (PCD) has paved the way for spectral x-ray computed tomography (spectral CT), which simultaneously measures a sample's linear attenuation coefficient (LAC) at multiple energies. However, cadmium telluride (CdTe)-based PCDs working under high flux suffer from detector effects, such as charge sharing and photon pileup. These effects result in the severe spectral distortions of the measured spectra and significant deviation of the extracted LACs from the reference attenuation curve. We analyze the influence of the spectral distortion correction on material classification performance. Approach: We employ a spectral correction algorithm to reduce the primary spectral distortions. We use a method for material classification that measures system-independent material properties, such as electron density, , and effective atomic number, . These parameters are extracted from the LACs using attenuation decomposition and are independent of the scanner specification. The classification performance with the raw and corrected data is tested on different numbers of energy bins and projections and different radiation dose levels. We use experimental data with a broad range of materials in the range of , acquired with a custom laboratory instrument for spectral CT. Results: We show that using the spectral correction leads to an accuracy increase of 1.6 and 3.8 times in estimating and , respectively, when the image reconstruction is performed from only 12 projections and the 15 energy bins approach is used. Conclusions: The correction algorithm accurately reconstructs the measured attenuation curve and thus gives better classification performance.

An algorithm to simulate nonstationary and non-Gaussian stochastic processes

We proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Densely sampled spectral modulation for x-ray CT using a stationary modulator with flying focal spot: a conceptual and feasibility study of scatter and spectral correction.

Modulation of the x-ray source in computed tomography (CT) by a designated filter to achieve a desired distribution of photon flux has been greatly advanced in recent years. In this work, we present a densely sampled spectral modulation (DSSM) as a promising low-cost solution to quantitative CT imaging in the presence of scatter. By leveraging a special stationary filter (namely a spectral modulator) and a flying focal spot, DSSM features a strong correlation in the scatter distributions across focal spot positions and sees no substantial projection sparsity or misalignment in data sampling, making it possible to simultaneously correct for scatter and spectral effects in a unified framework. The concept of DSSM is first introduced, followed by an analysis of the design and benefits of using the stationary spectral modulator with a flying focal spot (SMFFS) that dramatically changes the data sampling and its associated data processing. With an assumption that the scatter distributions across focal spot positions have strong correlation, a scatter estimation and spectral correction algorithm from DSSM is then developed, where a dual-energy modulator along with two flying focal spot positions is of interest. Finally, a phantom study on a tabletop cone-beam CT system is conducted to understand the feasibility of DSSM by SMFFS, using a copper modulator and by moving the x-ray tube position in the X direction to mimic the flying focal spot. Based on our analytical analysis of the DSSM by SMFFS, the misalignment of low- and high-energy projection rays can be reduced by a factor of more than 10 when compared with a stationary modulator only. With respect to modulator design, metal materials such as copper, molybdenum, silver, and tin could be good candidates in terms of energy separation at a given attenuation of photon flux. Physical experiments using a Catphan phantom as well as an anthropomorphic chest phantom demonstrate the effectiveness of DSSM by SMFFS with much better CT number accuracy and less image artifacts. The root mean squared error was reduced from 297.9 to 6.5 Hounsfield units (HU) for the Catphan phantom and from 409.3 to 39.2HU for the chest phantom. The concept of DSSM using a SMFFS is proposed. Phantom results on its scatter estimation and spectral correction performance validate our main ideas and key assumptions, demonstrating its potential and feasibility for quantitative CT imaging.

System-independent material classification through X-ray attenuation decomposition from spectral X-ray CT

We present a method for material classifications in spectral X-ray Computed Tomography (SCT) taking advantage of energy-resolving 2D detectors to simultaneously extract the energy dependence of a material’s linear attenuation coefficient (LAC). The method employs an attenuation decomposition presented by Alvarez et al., and estimates system-independent material properties of electron density (ρe) and effective atomic number (Zeff), independent of the scanner, from the energy-dependent LAC measurements. The method uses a spectral correction algorithm and the energy range is truncated to exclude bins with photon starvation and spectral distortion present even after correction of detector response. A novel technique of energy bin selection is used for optimized classification performance. The method is tested against another SCT classification method called SRZE for inspecting materials in the range of 6≤Zeff≤23. Our method aims at an increase in the speed of pot processing workflow after the data acquisition, and it achieves explicitly up to 32 times better time efficiency for the reconstruction with comparable accuracy for a range of materials important in threat detection.

VisNIR integrated multi-sensing penetrometer for in situ high-resolution vertical soil sensing

An in situ penetrometer system that can measure profile soil properties rapidly, cost-effectively, and at high vertical resolution would benefit the soil science and agriculture communities. A visible and near infrared (VisNIR) integrated multi-sensing penetrometer system was developed to automatically measure in situ soil VisNIR reflectance spectra, penetration resistance, and insertion depth along a soil profile. The system was tested in 11 agricultural fields in Nebraska, Illinois, Iowa, and South Dakota of the U.S. An independent soil VisNIR spectral library was used to build calibration models for soil property prediction. External Parameter Orthogonalization (EPO) was used to correct for the field intactness of in situ VisNIR spectra. The results showed that EPO was effective in correcting for the spectral disparity between in situ and dry-ground VisNIR spectra. The EPO correction showed an improvement of prediction accuracy of soil total carbon (R2 and RMSE improved from 0.29 and 3.06 % to 0.5 and 0.79 %, respectively) and total nitrogen (R2 and RMSE improved from 0.51 and 0.36 % to 0.62 and 0.06 %, respectively). The system also predicted soil bulk density with an RMSE of 0.12 g cm−3 and R2 of 0.80. It is concluded that the VisNIR multi-sensing penetrometer, along with the use of external soil spectral libraries and the spectral correction algorithm EPO, can lead to a rapid, robust and cost-effective system for in situ high resolution vertical soil sensing.

Method for system-independent material characterization from spectral X-ray CT

We propose a method for material characterization using Spectral X-ray Computed Tomography (SCT). Our SCT method takes advantage of recently-developed MultiX ME 100 photon counting detectors to simultaneously measure the energy dependence of a material's linear attenuation coefficient (LAC). Relative electron density (ρe) and effective atomic number (Ze) are estimated directly from the energy-dependent LAC measurements. The method employs a spectral correction algorithm and automated selection and weighting of the energy bins for optimized performance. When examining materials with Ze ≤ 23, this method achieves accuracy comparable to traditional dual-energy CT, which is often realized through consecutive data acquisitions, and is compatible with any spectral detector. The method disregards data in photon starved energy channels improving the detection of highly attenuating materials, compared to techniques that use energy integrating detectors.

Spectral correction algorithm for multispectral CdTe x-ray detectors

Compared to the dual-energy scintillator detectors widely used today, energy-resolved photon-counting x-ray detectors show the potential to improve material identification in various radiography and tomography applications used for industrial and security purposes. However, detector effects, such as charge sharing and photon pileup, distort the measured spectra in pixelated, photon-counting detectors operating under high flux. These effects result in a significant performance degradation of the detectors when used for material identification where accurate spectral measurements are required. We have developed a semianalytical, postdata acquisition, computational algorithm that corrects the measured attenuation curve for severe spectral distortions caused by the detector. The calibration of the algorithm is based on simple attenuation measurements of commercially available materials using standard laboratory sources, enabling the algorithm to be used in any x-ray setup. The algorithm is developed for correcting spectral data acquired with the MultiX ME100 CdTe x-ray detector but could be adapted with small adjustments to other photon-counting, energy-resolved detectors with CdTe sensors. The validation of the algorithm has been done using experimental data acquired with both a standard laboratory source and synchrotron radiation. The experiments show that the algorithm is fast, reliable at x-ray flux up to 5 Mph / s / mm2 and greatly improves the accuracy of the measured spectrally resolved linear attenuation, making the algorithm useful for both security and industrial applications where photon-counting detectors are used.

The Study of Spectral Correction Algorithm of Charge-Coupled Device Array Spectrometer

The charge-coupled device (CCD) array spectrometer is used for quick and simultaneous measurement of light spectrum. In scientific research and industrial application, the spectral correction algorithm is important to obtain the accurate values of photometry and chromaticity. The accuracy of spectrum depends on the correction of wavelength position, the linearity correction of CCD, the elimination of noise and dark current, the bandpass correction, the stray light correction, and the correction of frequency response. Many correction algorithms are studied to improve the CCD array spectrometer measurement. In this paper, we review and compare the correction algorithms from the past literature. Furthermore, we integrate them and find out an optimal algorithm to process the correction of spectrum measurement. The best results of luminous flux correction (ΔY) and chromatic correction (Δu'v') provide decreasing the difference of reference standard about 90%. The optimal correction algorithm provides a convenient method to enhance the measurement quality of CCD array spectrometer without changing the design of physical hardware.

Comparison of broadband and high-spectral resolution infrared observations

Abstract This note compares observations from two instruments with different spectral resolutions. The High-resolution Interferometer Sounder (HIS) observed radiances have a spectral resolution capable of differentiating individual absorption bands within the 600-2700cm− (3. 7-l7μ m) regime, the Earth Radiation Budget Experiment (ERBE) measures broadband (4-200μ m) longwave fluxes. To derive broadband fluxes, ERBE processing must account for the spectral response function of the scanning instrument. As the HIS has the spectral resolution to simulate various filter response functions, the HIS observations arc employed in a cross-validation of the spectral correction algorithm applied by the ERBE software processing. This is the only independent method of cross validating the first step in the processing of ERBE measurements. In addition, the HIS spectral measurements arc integrated and compared with the ERBE broadband longwave fluxes. These comparisons demonstrate the complimentary nature of the two instru...

The envelope of the error for trigonometric and Chebyshev interpolation

The error in Chebyshev or Fourier interpolation is the product of a rapidly varying factor with a slowly varying modulation. This modulation is the “envelope” of the error. Because this slow modulation controls the amplitude of the error, it is crucial to understand this “error envelope.” In this article, we show that the envelope varies strongly withx, but its variations can be predicted from the convergence-limiting singularities of the interpolated function f(x). In turn, this knowledge can be translated into a simple spectral correction algorithm for wringing more accuracy out of the same pseudospectral calculation of the solution to a differential equation.