Expressions for the calculation of isotropic Gaussian filter kernels in the spherical harmonic domain

Piretzidis, Dimitrios; Sideris, Michael G.

doi:10.1007/s11200-021-0272-9

Cited by 2 publications

(2 citation statements)

References 52 publications

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“…We compared the adaptive Savitzky-Golay filters performance with the other peer filtering methods including: Fourier transform [15], Gaussian Kernel filtering [16], Epanechnikov Kernel [17], Lowess [18] smoothing algorithms. In analysis, we use moving average optimal window length approach to compare the smoothing performance.…”

Section: Comparison Of Adaptive Savitzky-golay Filtering With Peer Me...mentioning

confidence: 99%

“…Therefore, an appropriate filtering method is necessary to filter the CNVs peaks. Several filtering methods have been proposing for peak processing, including spline smoothing [13], Stein's unbiased risk estimate (SURE) [14], Fourier transform [15], Gaussian Kernel filtering [16], Epanechnikov Kernel [17], Lowess [18], Savitzky-Golay [19] and discrete wavelet transform [20]. Some of those filtering methods experience computational challenges when handling highly corrupted signals.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Savitzky–Golay Filters for Analysis of Copy Number Variation Peaks from Whole-Exome Sequencing Data

et al. 2023

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Copy number variation (CNV) is a form of structural variation in the human genome that provides medical insight into complex human diseases; while whole-genome sequencing is becoming more affordable, whole-exome sequencing (WES) remains an important tool in clinical diagnostics. Because of its discontinuous nature and unique characteristics of sparse target-enrichment-based WES data, the analysis and detection of CNV peaks remain difficult tasks. The Savitzky–Golay (SG) smoothing is well known as a fast and efficient smoothing method. However, no study has documented the use of this technique for CNV peak detection. It is well known that the effectiveness of the classical SG filter depends on the proper selection of the window length and polynomial degree, which should correspond with the scale of the peak because, in the case of peaks with a high rate of change, the effectiveness of the filter could be restricted. Based on the Savitzky–Golay algorithm, this paper introduces a novel adaptive method to smooth irregular peak distributions. The proposed method ensures high-precision noise reduction by dynamically modifying the results of the prior smoothing to automatically adjust parameters. Our method offers an additional feature extraction technique based on density and Euclidean distance. In comparison to classical Savitzky–Golay filtering and other peer filtering methods, the performance evaluation demonstrates that adaptive Savitzky–Golay filtering performs better. According to experimental results, our method effectively detects CNV peaks across all genomic segments for both short and long tags, with minimal peak height fidelity values (i.e., low estimation bias). As a result, we clearly demonstrate how well the adaptive Savitzky–Golay filtering method works and how its use in the detection of CNV peaks can complement the existing techniques used in CNV peak analysis.

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Section: Comparison Of Adaptive Savitzky-golay Filtering With Peer Me...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Savitzky–Golay Filters for Analysis of Copy Number Variation Peaks from Whole-Exome Sequencing Data

et al. 2023

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Spherical harmonic coefficients of isotropic polynomial functions with applications to gravity field modeling

Piretzidis,

Kotsakis,

Mertikas

et al. 2023

J Geod

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Various aspects of gravity field modeling rely upon analytical mathematical functions for calculating spherical harmonic coefficients. Such functions allow quick and efficient evaluation of cumbersome convolution integrals defined on the sphere. In this work, we present a new analytical method for determining spherical harmonic coefficients of isotropic polynomial functions. This method in computationally flexible and efficient, since it makes use of recurrence relations. Also, its use is universal and could be extended to piecewise polynomials and polynomials with compact support. Our numerical investigation of the proposed method shows that certain recurrence relations lose accuracy as the order of implemented polynomials increases because of accumulation of numerical errors. Propagation of these errors could be mitigated by hybrid methods or using extended precision arithmetic. We demonstrate the relevance of our method in gravity field modeling and discuss two areas of application. The first one is the design of B-spline windows and filter kernels for the low-pass filtering of gravity field functionals (e.g., GRACE Follow-On monthly geopotential solutions). The second one is the calculation of spherical harmonic coefficients of isotropic polynomial covariance functions.

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Expressions for the calculation of isotropic Gaussian filter kernels in the spherical harmonic domain

Cited by 2 publications

References 52 publications

Adaptive Savitzky–Golay Filters for Analysis of Copy Number Variation Peaks from Whole-Exome Sequencing Data

Adaptive Savitzky–Golay Filters for Analysis of Copy Number Variation Peaks from Whole-Exome Sequencing Data

Spherical harmonic coefficients of isotropic polynomial functions with applications to gravity field modeling

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