Abstract:Source imaging maps back boundary measurements to underlying generators within the domain; e.g., retrieving the parameters of the generating dipoles from electrical potential measurements on the scalp such as in electroencephalography EEG). Fitting such a parametric source model is non-linear in the positions of the sources and renewed interest in mathematical imaging has led to several promising approaches
“…These results have then be extended to include more classes of acquisition devices (Dragotti et al 2007 ; Seelamantula and Unser 2008 ; Asl et al 2010 ; Tur et al 2011 ; Urigüen et al 2013 ) and more classes of signals (Maravić and Vetterli 2005 ; Berent et al 2010 ; Chen et al 2012 ). FRI sampling theory has also had impact in various applications (Baboulaz and Dragotti 2009 ; Poh and Marziliano 2010 ; Tur et al 2011 ; Kandaswamy et al 2013 ) and here we focus on an application in neuroscience. Fig.…”
The current methods used to convert analogue signals into discrete-time sequences have been deeply influenced by the classical Shannon–Whittaker–Kotelnikov sampling theorem. This approach restricts the class of signals that can be sampled and perfectly reconstructed to bandlimited signals. During the last few years, a new framework has emerged that overcomes these limitations and extends sampling theory to a broader class of signals named signals with finite rate of innovation (FRI). Instead of characterising a signal by its frequency content, FRI theory describes it in terms of the innovation parameters per unit of time. Bandlimited signals are thus a subset of this more general definition. In this paper, we provide an overview of this new framework and present the tools required to apply this theory in neuroscience. Specifically, we show how to monitor and infer the spiking activity of individual neurons from two-photon imaging of calcium signals. In this scenario, the problem is reduced to reconstructing a stream of decaying exponentials.
“…These results have then be extended to include more classes of acquisition devices (Dragotti et al 2007 ; Seelamantula and Unser 2008 ; Asl et al 2010 ; Tur et al 2011 ; Urigüen et al 2013 ) and more classes of signals (Maravić and Vetterli 2005 ; Berent et al 2010 ; Chen et al 2012 ). FRI sampling theory has also had impact in various applications (Baboulaz and Dragotti 2009 ; Poh and Marziliano 2010 ; Tur et al 2011 ; Kandaswamy et al 2013 ) and here we focus on an application in neuroscience. Fig.…”
The current methods used to convert analogue signals into discrete-time sequences have been deeply influenced by the classical Shannon–Whittaker–Kotelnikov sampling theorem. This approach restricts the class of signals that can be sampled and perfectly reconstructed to bandlimited signals. During the last few years, a new framework has emerged that overcomes these limitations and extends sampling theory to a broader class of signals named signals with finite rate of innovation (FRI). Instead of characterising a signal by its frequency content, FRI theory describes it in terms of the innovation parameters per unit of time. Bandlimited signals are thus a subset of this more general definition. In this paper, we provide an overview of this new framework and present the tools required to apply this theory in neuroscience. Specifically, we show how to monitor and infer the spiking activity of individual neurons from two-photon imaging of calcium signals. In this scenario, the problem is reduced to reconstructing a stream of decaying exponentials.
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