Filter Characteristics in Image Decomposition with Singular Spectrum Analysis

Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this viewpoint, the singular spectrum analysis can be understood as the adaptive and optimal generation of the filters and their two-step point-symmetric operation to the original data. In this paper, we point out that, when applied to the multidimensional data, the adaptively generated filters exhibit symmetry properties resulting from the bisymmetric nature of the lag-covariance matrices. The eigenvectors of the lag-covariance matrix are either symmetric or antisymmetric, and for the 2D image data, these lead to the differential-type filters with even- or odd-order derivatives. The dominant filter is a smoothing filter, reflecting the dominance of low-frequency components of the photo images. The others are the edge-enhancement or the noise filters corresponding to the band-pass or the high-pass filters. The implication of the decomposition to the image denoising is briefly discussed.

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MULTIDIMENSIONAL EXTENSION OF SINGULAR SPECTRUM ANALYSIS BASED ON FILTERING INTERPRETATION

Advances in Adaptive Data Analysis ◽

10.1142/s1793536914500058 ◽

2014 ◽

Vol 06 (01) ◽

pp. 1450005 ◽

Cited By ~ 3

Author(s):

KENJI KUME ◽

NAOKO NOSE-TOGAWA

Keyword(s):

Time Series ◽

Spectrum Analysis ◽

Arbitrary Dimension ◽

Singular Spectrum Analysis ◽

Simple Algorithm ◽

Image Data ◽

Multidimensional Data ◽

Data Series ◽

Singular Spectrum ◽

Original Time

Singular spectrum analysis is a nonparametric spectral decomposition of a time series. The singular spectrum analysis can be viewed as the two-step filtering with the complete set of eigenfilter adaptively constructed from the original time series. Based on this viewpoint, we present a flexible and quite simple algorithm for the singular spectrum analysis which can be applied to the multidimensional data series with arbitrary dimension. We have carried out the decomposition of two-dimensional image data, and the optimally constructed filters are found to be the smoothing or the edge enhancement filters of various type. We have also examined a simple example for the decomposition of 3D data.

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Multivariate Extension of the Singular Spectrum Analysis A New Tool in Understanding the Intraseasonal-Oscillation (ISO) of Philippines Summer Monsoon and its Association with Extreme Rainfall Events

Global NEST Journal ◽

10.30955/gnj.003202 ◽

2020 ◽

Keyword(s):

Spectrum Analysis ◽

Singular Spectrum Analysis ◽

Intraseasonal Oscillation ◽

Low Frequency ◽

Extreme Rainfall ◽

Active Phase ◽

Relative Strength ◽

Extreme Rainfall Events ◽

Singular Spectrum ◽

Increasing Trend

<p>The intraseasonal low-frequency oscillation is studied by using gridded rainfall dataset from 1979 to present. Multivariate Singular Spectrum Analysis (SSA) was used in the extraction of these modes. We have found out that there is a significant increasing trend in the relative strength of low frequency ISO. However, this happened only after the years 1979 to 1984 was removed in the trend analysis. A previous study found that the increased rainfall during the break and transition phase of low-frequency ISO could be a contributing factor to the decreasing trend during the active phase. In this study, the implication is rather the opposite - the increasing trend in rainfall, in terms of extreme events occurrence during the active phase of low-frequency ISO had been the contributor to the increasing trend of low-frequency ISO.</p>

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Shaped Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the EarlyDrosophilaEmbryo

BioMed Research International ◽

10.1155/2015/689745 ◽

2015 ◽

Vol 2015 ◽

pp. 1-14 ◽

Cited By ~ 4

Author(s):

Alex Shlemov ◽

Nina Golyandina ◽

David Holloway ◽

Alexander Spirov

Keyword(s):

Gene Expression ◽

Spectrum Analysis ◽

Expression Patterns ◽

Singular Spectrum Analysis ◽

Image Data ◽

Fruit Fly ◽

Biological Data ◽

Singular Spectrum ◽

Cylindrical Projection ◽

2D And 3D

In recent years, with the development of automated microscopy technologies, the volume and complexity of image data on gene expression have increased tremendously. The only way to analyze quantitatively and comprehensively such biological data is by developing and applying new sophisticated mathematical approaches. Here, we present extensions of 2D singular spectrum analysis (2D-SSA) for application to 2D and 3D datasets of embryo images. These extensions, circular and shaped 2D-SSA, are applied to gene expression in the nuclear layer just under the surface of theDrosophila(fruit fly) embryo. We consider the commonly used cylindrical projection of the ellipsoidalDrosophilaembryo. We demonstrate how circular and shaped versions of 2D-SSA help to decompose expression data into identifiable components (such as trend and noise), as well as separating signals from different genes. Detection and improvement of under- and overcorrection in multichannel imaging is addressed, as well as the extraction and analysis of 3D features in 3D gene expression patterns.

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