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Compressive Sensing for Transient Analysis
Dr. M. Sabarimalai Manikandan
CEN, Amrita University
Compressive Sensing
Compressed sensing is a new data acquisition theory that
aims to reduce the number of measurements required to
completely describe a signal by exploiting itscompletely describe a signal by exploiting its
compressibility or sparsity
The new model for signals utilized in CS is based on
sparse approximation
Sparse Signal Representation/Approximation
The signal can be represented or well approximated by
a linear combination of a small number of waveforms
taken from a basis or dictionary
There are numerous practical examples in which a signal
of interest is not sparse in an orthonormal basis.
The recovery of signals from undersampled data in the
common situation where such signals are not sparse in
an orthonormal basis or incoherent dictionary, but in a
truly redundant or overcomplete dictionary.
Compressive Sensing Requirements
Design of a stable measurement matrix that ensures
that the salient information in any K-sparse or
compressible signal is not damaged by the
dimensionality reduction.dimensionality reduction.
Develop a reconstruction algorithm to recover x from
the measurements y.
Sparse Signal Representation
Learning Overcomplete Dictionary
Dirac Functions
Heaviside Functions
Discrete Cosines
Discrete SinesDiscrete Sines
Hadamard-Walsh
Wavelets and Wavelet Packets
Dual-tree wavelets
Curvelets
Splines and Random vectors
Detection and Localization of Transient Signals
Transients are generally very short-duration nonstationary
signals often with oscillations.
impulsive and oscillatory transients
short-time energy, matched filters, higher-order statistics,
Fourier transform, Wigner-Vue distribution (WVD), S-
transform, wavelet and wavelet packet transforms
Limitations of traditional wavelet-based approaches
The common problem in well-known wavelet
transform-based methods is which mother wavelet
function and characteristic scale provides the best
time-frequency resolution for detection of transients.time-frequency resolution for detection of transients.
Detection and localization of transients is still a very
challenging task because the transients are typically
having different shapes, amplitudes, durations and
frequency content, which are not known in many
different applications and systems
Applications of Transient Analysis
Power-quality analysis
Underwater acoustics system
Audio and biosignal analysis
Ultra wideband (UWB) pulsed radar
Mechanical fault diagnosis
Seismic signal analysis
Transient Representation
CS-Based Transient Detection Algorithm
Detection of Oscillatory Transients
Detection of Spikes
CS-based Detection
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Advantages of CS-Based Approach
In addition to time information, the CS-based detector
also preserves essential characteristics of the transients
(amplitude, frequency and shape) that wavelet-based(amplitude, frequency and shape) that wavelet-based
method may fail to preserve.
This is a clear advantage of our CS-based method over
the wavelet-based methods.
Phase Shift Detection and Correction
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50 Hz sinusoidal signal with phase shift of 32 degree
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150 Hz sinusoidal signal without phase shift
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Powerline Frequency Removal
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original ECG signal
original ECG signal plus powerline
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original ECG signal
original ECG signal plus powerline (10 degree)
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original ECG signal plus powerline
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Output of CS-based approach
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original ECG signal plus powerline (10 degree)
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Output of CS-based approach
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50 Hz Powerline Removal
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original ECG signal
original ECG signal plus powerline (10 degree)
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original ECG signal
original ECG signal plus powerline (86 degree)
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original ECG signal plus powerline (10 degree)
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Output of CS-based approach
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original ECG signal plus powerline (86 degree)
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Output of CS-based approach
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Simultaneous Removal of 50 Hz and LF Artifact
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original ECG signal
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original ECG signal plus powerline
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Output of CS-based approach
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Output of CS-based baseline wander removal
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Detection and Localization of Transient Signals
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DCT:Localization
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Reconstruction
