Wavelets in neuroscience

Foreword
Preface
Contents
Acronyms
1 Mathematical Methods of Signal Processing in Neuroscience
	1.1 General Remarks
	1.2 Nonstationarity of Neurophysiological Data
	1.3 Wavelets in Basic Sciences and Neuroscience
	1.4 Automatic Processing of Experimental Data in Neuroscience
	1.5 Brain-Computer Interfaces
	1.6 Topics to Consider
	References
2 Brief Tour of Wavelet Theory
	2.1 From Fourier Analysis to Wavelets
	2.2 Continuous Wavelet Transform
		2.2.1 Main Definitions. Properties of the Continuous Wavelet Transform
		2.2.2 Mother Wavelets
		2.2.3 Numerical Implementation of the Continuous Wavelet Transform
		2.2.4 Visualisation of Wavelet Spectra. Wavelet Spectra of Model Signals
		2.2.5 Phase of the Wavelet Transform
	2.3 Discrete Wavelet Transform
		2.3.1 Comparison of the Discrete and Continuous Wavelet Transforms
		2.3.2 General Properties
	References
3 Analysis of Single Neuron Recordings
	3.1 Introduction
	3.2 Wavelet Analysis of Intracellular Dynamics
		3.2.1 Interference Microscopy and Subcellular Dynamics
		3.2.2 Modulation of High Frequency Oscillation by Low Frequency Processes
		3.2.3 Double Wavelet Transform and Analysis of Modulation
		3.2.4 Modulation of Spike Trains by Intrinsic Neuron Dynamics
	3.3 Information Encoding by Individual Neurons
		3.3.1 Vibrissae Somatosensory Pathway
		3.3.2 Classification of Neurons by Firing Patterns
		3.3.3 Drawbacks of the Traditional Approach to Information Processing
		3.3.4 Wavelet Transform of Spike Trains
		3.3.5 Dynamical Stability of the Neuronal Response
		3.3.6 Stimulus Responses of Trigeminal Neurons
	3.4 Wavelet Coherence for Spike Trains: A Way to Quantify Functional Connectivity
		3.4.1 Wavelet Coherence of Two Point Processes
		3.4.2 Measure of Functional Coupling Between Stimulus and Neuronal Response
		3.4.3 Functional Connectivity of Gracilis Neurons to Tactile Stimulus
	References
4 Classification of Neuronal Spikes from Extracellular Recordings
	4.1 Introduction
	4.2 General Principles of Spike Sorting
	4.3 Spike Detection Over a Broadband Frequency Activity
	4.4 Naive Spike Sorting
	4.5 Principal Component Analysis as Spike-Feature Extractor
		4.5.1 How It Works
		4.5.2 Possible Pitfalls
	4.6 Wavelet Transform as Spike-Feature Extractor
		4.6.1 Wavelet Spike Classifier
		4.6.2 Potential Problems
	4.7 Wavelet Shape-Accounting Classifier
	4.8 Performance of PCA Versus WT for Feature Extraction
	4.9 Sensitivity of Spike Sorting to Noise
		4.9.1 Impact of High/Low Frequency Noise on PCA and WT
		4.9.2 Proper Noise Filtering May Improve Spike Sorting
	4.10 Optimal Sorting of Spikes with Wavelets and Adaptive Filtering
		4.10.1 Noise Statistics and Spike Sorting
		4.10.2 Parametric Wavelet Sorting with Advanced Filtering
	4.11 Spike Sorting by Artificial Neural Networks
		4.11.1 General Approach
		4.11.2 Artificial Neural Networks
		4.11.3 Training the Artificial Neural Network
		4.11.4 Algorithm for Spike Sorting Using Neural Networks
	4.12 Artificial Wavelet Neural Networks for Spike Sorting
		4.12.1 Structure of Wavelet Neural Networks
		4.12.2 Wavelet Neural Networks
	References
5 Analysis of Gamma-Waves in Multielectrode LFP Recordings
	5.1 Introduction
	5.2 Disentanglement of Raw LFP Recordings into Pathway-Specific Generators
		5.2.1 LFP Recordings and Current-Source-Density Analysis
		5.2.2 Decomposition of LFPs into Pathway-Specific Generators
	5.3 Localization and Quantification of Gamma Waves in the Schaffer-Generator …
		5.3.1 Method for Detecting Gamma Waves
		5.3.2 Elementary Micro-fEPSPs in Ongoing Schaffer Activity
		5.3.3 Detected Gamma Events Help to Establish Causal Relations Between CA3 and CA1 Pyramidal Cells
	5.4 Improved Identification of Micro-fEPSP Events
		5.4.1 Distortion of Micro-fEPSP Events by Wavelet Method
		5.4.2 Likelihood Enhanced Wavelet (LeW) Method
	5.5 Bilateral Integration of Gamma-Parsed Information
		5.5.1 Experimental Recordings and Retrieval of Bilateral Micro-fEPSP Events
		5.5.2 Analysis of Bilateral CA3-CA1 Pathways
	5.6 Conclusions
	References
6 Wavelet Approach to the Study of Rhythmic Neuronal Activity
	6.1 Introduction
	6.2 Basic Principles of Electroencephalography
		6.2.1 Electrical Biopotential: From Neuron to Brain
		6.2.2 Application of EEG in Epilepsy Research
	6.3 General Principles of Time–Frequency Analysis of EEG
		6.3.1 The Need for Mathematical Analysis of EEG
		6.3.2 Time–Frequency Analysis of EEG: From Fourier Transform to Wavelets
		6.3.3 Time–Frequency Analysis of Spike-Wave Discharges by Means of Different Mother Wavelets
	6.4 Applications of Wavelets in Electroencephalography
		6.4.1 Time–Frequency Analysis of EEG Structure
		6.4.2 Automatic Detection of Oscillatory Patterns and Different Rhythms in Pre-recorded EEG
		6.4.3 Classification of Oscillatory Patterns
		6.4.4 Real-Time Detection of Oscillatory Patterns in EEG
		6.4.5 Multichannel EEG Analysis of Synchronization of Brain Activity
		6.4.6 Artifact Suppression in Multichannel EEG Using Wavelets and Independent Component Analysis
		6.4.7 Study of Cognitive Processes
	References
7 Wavelet-Based Diagnostics of Paroxysmal Activity in EEG and Brain-Computer Interfaces for Epilepsy Control
	7.1 Introduction
	7.2 Mother Wavelet Function in the Continuous Wavelet Transform
	7.3 Detection of Spike-Wave Discharges (Absence Epilepsy) in WAG/Rij Rats
	7.4 Spindle-Like Oscillations and Spike-Wave Epilepsy
		7.4.1 Time–Frequency Analysis of Spindle-Like Oscillatory Patterns
		7.4.2 Wavelet-Based Approach for Detecting Sleep Spindles and 5–9 Hz Oscillations in EEG
		7.4.3 Classification of Normal and Abnormal Spindle Oscillations by Means of Adaptive Wavelet Analysis
	7.5 Pro-epileptic Activity and Undeveloped Spike-Wave Seizures …
		7.5.1 Time–Frequency Characteristics of Pro-epileptic Patterns in EEG in WAG/Rij Rats
		7.5.2 Algorithm for the Automatic Detection of Pro-epileptic Patterns in EEG
	7.6 Brain-Computer Interface for On-Line Diagnostics of Epileptic Seizures
		7.6.1 On-Line SWD Detection Algorithm
		7.6.2 Experimental Verification of the Algorithm and On-Line SWD Diagnostics
	7.7 Brain Stimulation Brain-Computer Interface for Prediction and Prevention …
		7.7.1 Precursor Wavelet-Based On-Line Detection
		7.7.2 Absence Seizure Control by a Brain Computer Interface
	References
8 Analysis of Visual Sensory Processing in the Brain and Brain-Computer Interfaces for Human Attention Control
	8.1 Introduction
	8.2 Ambigous Stimuli as a Tool to Study Visual Perception
	8.3 Local and Integrative Neural Activity During Visual Sensory Processing
		8.3.1 Local Activity
		8.3.2 Functional Connectivity
	8.4 Visual Sensory Processing and the Human Factors
		8.4.1 Different Scenarios of Visual Perception
		8.4.2 Spectral Properties of the Different Scenarios
		8.4.3 Single-Trial Analysis
	8.5 BCIs for the Control of Human Condition During Sensory Processing Tasks
		8.5.1 Wavelet-Based Approach to Estimate Attention in BCI
		8.5.2 Testing the Feedback Effect
		8.5.3 Cognitive Load Distribution via BCI
	References
9 Analysis and Real-Time Classification of Motor-Related EEG and MEG Patterns
	9.1 Real and Imagery Movements
		9.1.1 Wavelet-Transform Modulus Maxima (WTMM)
		9.1.2 Time–Frequency Analysis
	9.2 Visual and Kinestetic Motor Imagery
		9.2.1 Wavelet Analysis
		9.2.2 Cluster Analysis
		9.2.3 Neurophysiological Aspects of Motor Imagery
	9.3 Age-Related Distinctions in EEG Signals During Execution …
		9.3.1 Experimental Study and Motor Brain Response Time Analysis
		9.3.2 Time–Frequency Analysis of Brain Response on Motor Activity
		9.3.3 Classification of Wavelet Spectra by Machine Learning Techniques
	References
10 Conclusion
	Reference