Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about (i) parameterizing the intermediate temporal scale levels, (ii) analysing the resulting temporal dynamics, (iii) transferring the theory to a discrete implementation, (iv) computing scale-normalized spatio-temporal derivative expressions for spatio-temporal feature detection and (v) computational modelling of receptive fields in the lateral geniculate nucleus (LGN) and the primary visual cortex (V1) in biological vision. We show that by distributing the intermediate temporal scale levels according to a logarithmic distribution, we obtain much faster temporal response properties (shorter temporal delays) compared to a uniform distribution. Specifically, these kernels converge very rapidly to a limit kernel possessing true self-similar scale-invariant properties over temporal scales, thereby allowing for true scale invariance over variations in the temporal scale, although the underlying temporal scale-space representation is based on a discretized temporal scale parameter. We show how scale-normalized temporal derivatives can be defined for these time-causal scale-space kernels and how the composed theory can be used for computing basic types of scale-normalized spatio-temporal derivative expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and Vision, published online Dec 201

The effect of voluntary modulation of the sensory-motor rhythm during different mental tasks on H reflex

Objectives: The aim of this study was to explore the possibility of the short-term modulation of the soleus H reflex through self-induced modulation of the sensory-motor rhythm (SMR) as measured by electroencephalography (EEG) at Cz. Methods: Sixteen healthy participants took part in one session of neuromodulation. Motor imagery and mental math were strategies for decreasing SMR, while neurofeedback was used to increase SMR. H reflex of the soleus muscle was elicited by stimulating tibial nerve when SMR reached a pre-defined threshold and was averaged over 5 trials. Results: Neurofeedback and mental math both resulted in the statistically significant increase of H reflex (p = 1.04·10− 6 and p = 5.47·10− 5 respectively) while motor imagery produced the inconsistent direction of H reflex modulation (p = 0.57). The average relative increase of H reflex amplitude was for neurofeedback 19.0 ± 5.4%, mental math 11.1 ± 3.6% and motor imagery 2.6 ± 1.0%. A significant negative correlation existed between SMR amplitude and H reflex for all tasks at Cz and C4. Conclusions: It is possible to achieve a short-term modulation of H reflex through short-term modulation of SMR. Various mental tasks dominantly facilitate H reflex irrespective of direction of SMR modulation. Significance: Improving understanding of the influence of sensory-motor cortex on the monosynaptic reflex through the self-induced modulation of cortical activity