Wavelet denoising of powder diffraction patterns

Wavelet theory has already achieved huge success. For Secondary Ions Mass Spectrometry (SIMS) signals, denoising the secondary signal, which is altered by the measurement, is considered that an essential step prior to applying such a signal processing technique that aims enhance the SIMS signals.The most efficient and widely used wavelet denoising method is based on wavelet coefficient thresholding. This process involves three important steps; wavelet decomposition: the input signals are decomposed into wavelet coefficients, thresholding: the wavelet coefficients are modified according to a threshold, and reconstruction: the modified coefficients are used in an inverse transform to obtain the noise-free-signal. Several researchers have used thresholding wavelet denoising techniques. The choice of wavelet type and the level of resolution can have a significant influence; it is important to note that the choice of resolution level depends on the type of signal we are dealing with, the nature of the present noise, and our specific goals for the denoised signal. It is generally recommended to test different resolution levels and evaluate their impact on the quality of the denoised signal before making a final decision. Moreover, the results obtained in wavelet denoising can be significantly influenced by the selection of wavelet types. The chosen wavelet type plays a crucial role in the extraction of signal details. Indeed, the effectiveness of denoising the MD6 sample has been demonstrated by the results obtained with sym4, db8, Haar and coif5 wavelets? These wavelets have effectively reduced noise while preserving crucial signal information, leading to an enhancement in the quality of the denoised signal.

Wavelet denoising is commonly used for speech enhancement because of the simplicity of its implementation. However, the conventional methods generate the presence of musical residual noise while thresholding the background noise. The unvoiced components of speech are often eliminated from this method. In this paper, a novel algorithm of wavelet coefficient threshold (WCT) based on time-frequency adaptation is proposed. In addition, an unvoiced speech enhancement algorithm is also integrated into the system to improve the intelligibility of speech. The wavelet coefficient threshold (WCT) of each subband is first temporally adjusted according to the value of a posterior signal-to-noise ratio (SNR). To prevent the degradation of unvoiced sounds during noise, the algorithm utilizes a simple speech/noise detector (SND) and further divides speech signal into unvoiced and voiced sounds. Then, we apply appropriate wavelet thresholding according to voiced/unvoiced (V/U) decision. Based on the masking properties of human auditory system, a perceptual gain factor is adopted into wavelet thresholding for suppressing musical residual noise. Simulation results show that the proposed method is capable of reducing noise with little speech degradation and the overall performance is superior to several competitive methods.

On the block thresholding wavelet estimators with censored data

Thresholding of empirical wavelet coefficients was discussed in Section 7.1, along with some examples of global thresholds. This chapter will pick up where Section 7.1 left off, focusing on the nonparametric regression situation. The ideas described here could also be adapted for use in density estimation or other types of function estimation. To focus attention on the methods described in this chapter, it will be assumed throughout that an orthogonal wavelet transform on the unit interval is used, and that the sample size is a power of two: n = 2J for some integer J > 0. When this condition is not met, the methods described herein may be adapted, using techniques described in Chapter 6.KeywordsWavelet CoefficientThreshold SelectionGlobal ThresholdWavelet EstimatorShrinkage FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients.

We consider the wavelet-based estimators of mean regression function with long memory moving average errors and investigate their asymptotic rates of convergence based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates within a logarithmic term over a large range of Besov function classes \(B^{s}_{p,q}\). Therefore, in the presence of long memory non-Gaussian moving average noise, wavelet estimators still achieve nearly optimal convergence rates and provide explicitly the extraordinary local adaptability. The theory is illustrated with some numerical examples.

A new method for image denoising was presented，which colligated the strong point of wave atoms transform and Cycle Spinning. Due to lack of translation invariance of wave atoms transform，image denoising by coefficient thresholding would lead to Pseudo-Gibbs phenomena. Cycle Spinning was employed to avoid the artifacts. Experimental results show that the method can remove noisy and remain edges, while Pseudo-Gibbs phenomena are controlled efficiently, and can get better visual effect and PSNR gains compared with the methods like simplex wave atoms or wavelet denoising using Cycle Spinning.And in heavy background noise, this advantage is significant.

Two techniques are presented for the extraction of the individual intensities of completely overlapping reflections in a powder diffraction pattern. The first is analogous to Sayre's [Acta Cryst. (1952). 5, 60–65] squaring method while the second is based upon maximizing the entropy of the Patterson function subject to the constraints imposed by the observed intensities of single and overlapping groups of reflections. Although both methods are superior to a simple equipartition of intensities amongst overlapping reflections, the maximum-entropy (ME) technique is the more robust and scientifically justifiable. The ME Patterson map extracts the maximum amount of information from the available observed intensities and is thus optimal for Patterson-technique structure determination from powder diffraction patterns. The agreement between true |F|2 values of overlapping reflections and the values obtained by maximum entropy is, in most simulated cases, excellent.

A method is described for filtering magnetotelluric (MT) data in the wavelet domain that requires a minimum of human intervention and leaves good data sections unchanged. Good data sections are preserved because data in the wavelet domain is analyzed through hierarchies, or scale levels, allowing separation of noise from signals. This is done without any assumption on the data distribution on the MT transfer function. Noisy portions of the data are discarded through thresholding wavelet coefficients. The procedure can recognize and filter out point defects that appear as a fraction of unusual observations of impulsive nature either in time domain or frequency domain. Two examples of real MT data are presented, with noise caused by both meteorological activity and power-line contribution. In the examples given in this paper, noise is better seen in time and frequency domains, respectively. Point defects are filtered out to eliminate their deleterious influence on the MT transfer function estimates. After the filtering stage, data is processed in the frequency domain, using a robust algorithm to yield two sets of reliable MT transfer functions.

We described an adaptive denoising method to improve image quality in a wavelet-based image compression process that uses dithered quantization. In our method, the second-order moment of the quantization noise is made independent of the signal by random quantization. Then, the quantization noise is reduced by thresholding wavelet coefficients. We first obtained a fixed threshold using any known technique. Then, a neighborhood is searched for the optimal threshold to optimize some cost function.

This paper presents a double wavelet denoising (DWAD) method, which can preserve more details of an original signal. Although the noise removal method based on wavelet transform has been widely used, it still performs poorly for the signals with a low signal-to-noise ratio (SNR) or frequency overlap. Different from the wavelet denoising methods based on a single basis function, the DWAD considers filtering the wavelet coefficients of the noisy signal by threshold functions under two different wavelet domains, simultaneously. It considers using the difference of wavelet coefficient distribution and forcing the denoised signals under two wavelet domains to be the same to achieve more retention of details. In addition, the arctangent function is employed as a penalty function for wavelet coefficients to induce strong sparse wavelet coefficients. The DWAD is applied to one-dimensional signals and it is found that some wavelet coefficients which are smaller than the threshold could be retained during noise removal. The experiment results show that the average SNR of different noise levels is improved by at least 4.2 and 2.1 dB compared with the classical soft threshold method for the one-dimensional and image signals, respectively. Besides, the DWAD tends to obtain better performance on the details of original signals.

Phase diagrams and X-ray powder diffraction patterns provide critical information for thermoelectric (TE) research. We have conducted a survey of phase diagrams and powder diffraction patterns of TE systems in the ASM (American Society for Metals) Metal/Alloy database and ICDD (International Centre for Diffraction Data) PDF (Powder Diffraction File), respectively, for their availability and crystal systems. In this report, we focus on TE materials that have the half-HeuslerXYZstructure, and related compounds, based on a set of materials selection rules. We found that among 306 potentialXYZcompounds that we have surveyed, 234 have powder diffraction patterns in the PDF, but only 28 have phase diagram information, and 67 do not have any crystallographic information. Among the 234 phases with powder patterns, 84 were reported to have cubicF43mhalf-Heusler type structure, and the remainder have hexagonal, orthorhombic or other structure types. SomeXYZcompounds have both cubic and hexagonal phases. This information will provide the basis for future activities for the improvement of the databases. These activities include filling the missing gaps in both phase equilibria database and the PDF, as well as adding TE and pertinent physical properties to the PDF.

From powder pattern indexing it has been demonstrated that [Y(H(2)O)](2)(C(2)O(4))(CO(3))(2), yttrium oxalate carbonate, crystallizes with orthorhombic symmetry, space group C222(1), a = 7. 8177 (7), b = 14.943 (1), c = 9.4845 (7) A, V = 1108.0 (1) A(3), Z = 4. This unit cell displays a doubling of the c parameter, arising from weak diffraction lines observed in the powder diffraction pattern, with respect to results reported in the literature. The crystal structure has been solved ab initio using direct methods from powder data and has been confirmed by additional single-crystal data collected with a CCD area detector. The overall crystal structure is similar for both unit cells, except that an alternation of the carbonate groups in the direction parallel to the screw axis is displayed in the larger cell, while with the suggested half unit cell (space group C2mm) the carbonate groups would show only one orientation. The unit-cell determination strategy from single-crystal diffraction, collected with Nonius CAD-4 and Nonius Kappa CCD diffractometers, is discussed with respect to the results extracted from the powder diffraction pattern. The study demonstrates the power and usefulness of the full trace of a powder pattern for the detection of subtle structure details.

The objective of this study was to analyze the content of γ-aminobutyric acid (GABA) in germinated brown rice (GBR) by using near-infrared spectroscopy (NIRS) and the pretreatment method of wavelet de-noising (WD). The prediction accuracy of the NIRS model established by the Daubechies5 wavelet basis function at 3 level denoising treatment is the highest, the correlation coefficient for calibration (rc) is 0.931, the root mean square error of calibration (RMSEC) is 0.4038 mg/100 g, the Bias of calibration is 0.006, the correlation coefficient for prediction (rp) is 0.916, the root mean square error of prediction (RMSEP) is 0.4329 mg/100 g, the Bias of prediction is 0.010, and the ratio of performance to deviation (RPD) is 4.911. Results showed that the predicted and actual values had high correlation. Therefore, these results indicate that the NIRS model treated by WD is feasible to detect GABA content in GBR rapidly and nondestructively. Keywords: near-infrared spectroscopy, wavelet transformation, germinated brown rice, γ-aminobutyric acid, quantitative analysis DOI: 10.25165/j.ijabe.20211403.6178 Citation: Zhang Q, Liu N, Wang S S, Pan L Q. Nondestructive determination of GABA in germinated brown rice with near infrared spectroscopy based on wavelet transform denoising. Int J Agric & Biol Eng, 2021; 14(3): 200–206.

The main difficulty in multiscale product thresholding is to determine a proper threshold. In this paper, a hard thresholding function applied to multiscale product is constructed in the product form of shrinkage coefficient function and wavelet coefficients. This function is infinite-order differentiable with respect to wavelet coefficient, and can adaptively shrink wavelet coefficient in the neighborhood of the threshold. Furthermore, minimizing the Stein unbiased risk estimate (SURE) based on the thresholding function, the optimal threshold value is obtained in the mean square error (MSE) sense. In simulations to denoise multiple classic noisy signals, the traditional multiscale product coefficient thresholding is improved through using our optimal threshold.