Adaptive singular spectrum analysis for seismic denoising and interpolation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V133-V142 ◽  
Author(s):  
Hojjat Haghshenas Lari ◽  
Mostafa Naghizadeh ◽  
Mauricio D. Sacchi ◽  
Ali Gholami
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Singular Spectrum Analysis ◽  
Computational Cost ◽  
Hankel Matrix ◽  
Real Data ◽  
Singular Spectrum ◽  
Value Decomposition ◽  
Spatially Varying ◽  
Spatial Patches

We have developed an adaptive singular spectrum analysis (ASSA) method for seismic data denoising and interpolation purposes. Our algorithm iteratively updates the singular-value decomposition (SVD) of current spatial patches using the most recently added spatial sample. The method reduces the computational cost of classic singular spectrum analysis (SSA) by requiring QR decompositions on smaller matrices rather than the factorization of the entire Hankel matrix of the data. A comparison between results obtained by the ASSA and SSA methods, in which the SVD applies to all of the traces at once, proves that the ASSA method is a valid way to cope with spatially varying dips. In addition, a comparison of the ASSA method with the windowed SSA method indicates gains in efficiency and accuracy. Synthetic and real data examples illustrate the effectiveness of our method.

Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. V25-V32 ◽  
Author(s):  
Vicente Oropeza ◽  
Mauricio Sacchi
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Field Data ◽  
Convex Sets ◽  
Singular Spectrum Analysis ◽  
Hankel Matrix ◽  
Reconstruction Method ◽  
Rank Reduction ◽  
Data Set ◽  
Singular Spectrum

We present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records. We based our technique on multichannel singular spectrum analysis (MSSA). The technique entails organizing spatial data at a given temporal frequency into a block Hankel matrix that in ideal conditions is a matrix of rank [Formula: see text], where [Formula: see text] is the number of plane waves in the window of analysis. Additive noise and missing samples will increase the rank of the block Hankel matrix of the data. Consequently, rank reduction is proposed as a means to attenuate noise and recover missing traces. We present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets. In addition, we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm. We apply MSSA reconstruction to synthetic examples and a field data set. Synthetic examples were used to assess the performance of the method in two reconstruction scenarios: a noise-free case and data contaminated with noise. In both cases, we found extremely low reconstructions errors that are indicative of an optimal recovery. The field data example consists of a 2D prestack volume that depends on common midpoint and offset. We use the MSSA reconstruction method to complete missing offsets and, at the same time, increase the signal-to-noise ratio of the seismic volume.

Computational efficient multidimensional singular spectrum analysis for prestack seismic data reconstruction

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. V111-V119 ◽  
Author(s):  
Jinkun Cheng ◽  
Mauricio Sacchi ◽  
Jianjun Gao
Keyword(s):  
Spectrum Analysis ◽  
Seismic Data ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Data Reconstruction ◽  
Hankel Matrices ◽  
Computational Costs ◽  
Singular Spectrum ◽  
Seismic Data Reconstruction ◽  
Memory Efficient

We have evaluated a fast and memory efficient implementation of the multidimensional singular spectrum analysis (MSSA) method for seismic data reconstruction. The new algorithm makes use of random projections and the structure of Hankel matrices to avoid the construction of large Hankel trajectory matrices. Through tests with synthetic and real data examples, we find that the presented algorithm significantly decreases the computational costs of MSSA seismic data recovery without compromising its accuracy.

Non-Negative Time Series Reconstruction via Singular Spectrum Analysis: A Case Study of Precipitation Dynamics in Nigeria

2020 ◽  
Vol 19 (04) ◽  
pp. 2050045
Author(s):  
Olushina Olawale Awe ◽  
Rahim Mahmoudvand ◽  
Paulo Canas Rodrigues
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Real Data ◽  
Series Data ◽  
Monthly Precipitation ◽  
Singular Spectrum ◽  
Value Decomposition ◽  
Negative Time

A proper understanding and analysis of the processes involved in seasonal precipitation variability and dynamics is essential to provide reliable information about climate change and how it can affect matters of critical importance such as water availability and agricultural productivity in urban cities. Precipitation data, as many other time series data present only non-negative observations, are is not constrained by standard time series methods. In this paper, we propose a modified singular spectrum analysis (SSA) algorithm for decomposition and reconstruction of time series with non-negative values. Our approach uses a non-negative matrix factorization (NMF) instead of the singular value decomposition in the SSA algorithm. The new algorithm is compared with the classic SSA algorithm by considering a simulation study and observed data of monthly precipitation of four major cities in Nigeria (Lagos, Kano, Ibadan and Kaduna). Although in terms of mean stared errors both methods give similar results, the percentage of negative fitted values for reconstructions with the classical SSA algorithm reached more than [Formula: see text] in our real data application, which is inappropriate for non-negative time series. The proposed adaptation of the SSA algorithm for non-negative time series data provides an important development with applications in many fields where time series data has non-negative constraints.

INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION

2012 ◽  
Vol 04 (04) ◽  
pp. 1250023 ◽  
Author(s):  
KENJI KUME
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Original Time Series ◽  
Singular Vectors ◽  
Singular Spectrum ◽  
Original Time ◽  
Value Decomposition ◽  
Insight Into

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

Additive Decomposition of Power Spectrum Density in Singular Spectrum Analysis

2016 ◽  
Vol 08 (01) ◽  
pp. 1650003
Author(s):  
Kenji Kume ◽  
Naoko Nose-Togawa
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Power Spectrum Density ◽  
Spectral Structure ◽  
Additive Decomposition ◽  
Singular Spectrum ◽  
Spectrum Density ◽  
Value Decomposition

Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging lead to a time-series decomposition. In this paper, we propose an novel algorithm for the additive decomposition of the power spectrum density of a time series based on the filtering interpretation of SSA. This can be used to examine the spectral overlap or the admixture of the SSA decomposition. We can obtain insights into the spectral structure of the SSA decomposition which helps us for the proper choice of the window length in the practical application. The relationship to the conventional SSA decomposition of a time series is also discussed.

scholarly journals A Low-Complexity Model-Free Approach for Real-Time Cardiac Anomaly Detection Based on Singular Spectrum Analysis and Nonparametric Control Charts

2017 ◽  
Author(s):  
Michael Lang
Keyword(s):  
Real Time ◽  
Spectrum Analysis ◽  
Control Charts ◽  
Singular Spectrum Analysis ◽  
Computational Cost ◽  
Cardiac Anomaly ◽  
Cardiac Anomalies ◽  
Singular Spectrum ◽  
Model Free ◽  
Model Free Approach

While the importance of continuous monitoring of electrocardiographic (ECG) or photoplethysmographic (PPG) signals to detect cardiac anomalies is generally accepted in preventative medicine, there remain major barriers to its actual widespread adoption. Most notably, current approaches tend to lack real-time capability, exhibit high computational cost, and be based on restrictive modeling assumptions or require large amounts of training data. We propose a lightweight and model-free approach for the online detection of cardiac anomalies such as ectopic beats in ECG or PPG signals based on the change detection capabilities of Singular Spectrum Analysis (SSA) and nonparametric rank-based cumulative sum (CUSUM) control charts. The procedure is able to quickly detect anomalies without requiring the identification of fiducial points such as R-peaks and is computationally significantly less demanding than previously proposed SSA-based approaches. Therefore, the proposed procedure is equally well suited for standalone use and as an add-on to complement existing (e.g. heart rate (HR) estimation) procedures.

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