Description

1.1 Technological advances in neuroimaging
Recent advances in high-density imaging and optical voltage sensors now allow the observation of neuronal and glial activity with unprecedented spatial and temporal resolution. We leveraged the experiments of R. Prevedel to develop a generic method for reconstructing spatially organized neuronal subnetworks from volumetric three-dimensional calcium imaging using graph theory. In particular, we identified columnar-like microcircuits in the primary motor cortex, exhibiting a characteristic information flow structure (Aymard et al., 2025).

In parallel, genetically encoded voltage indicators (GEVI/GEDI) provide direct access to membrane potential variations, particularly in astrocytes. However, these data pose major challenges: the signal is indirect (fluorescence rather than electrical potential), highly noisy, and biologically relevant events may be confounded with extreme fluctuations of the noise.

1.2 The fundamental problem: distinguishing signal from noise
Our preliminary results on the analysis of GEDI recordings in astrocytes revealed a fundamental difficulty: classical event detection methods (filtering, peak detection based on prominence, spectral analysis) fail to reliably distinguish biological events from extreme fluctuations generated by the Poisson noise inherent to optical measurements.
The analysis of the distributions of detected event features (rise time, decay time, amplitude, duration) suggests a Poisson–Gaussian noise model. Furthermore, the detected event rate is strongly correlated with the baseline signal intensity, indicating that many false positives remain even after filtering.
The central question of this thesis is therefore: how can one distinguish a biological event from an extreme noise event, and how can this distinction be exploited to reconstruct the underlying neuronal networks?

2. Mathematical modeling (to be developed)
2.1 Model of the observed signal

The observed signal will be modeled using the additive decomposition:
Y(t)=B(t)+S(t)+ε(t)
where
B(t) represents a slow drift (photobleaching, tissue motion),
S(t) is the latent signal associated with neuronal or glial activity, and
ε(t) is a stochastic process modeling noise.

In the case of optical photon-counting measurements, the noise is naturally modeled as a Poisson–Gaussian process:
Y(t)∼Poisson(λ(t))+ηG(t) (t)
where ηG represents thermal Gaussian noise. This model implies a signal-dependent variance:
Var(Y(t))≈λ(t) which necessitates the use of a variance-stabilizing transformation such as the Anscombe transform: Z(t)=2Y(t)+38
2.2 Effect of spatial aggregation

A fundamental exploitable property is the differential behavior of noise and signal under spatial aggregation. For an average over n pixels:
Yˉn(t)=1n∑Yi(t) whereas a spatially coherent signal does not follow this scaling law. This property can therefore be used to discriminate biological structures from noise.

Skills required

Probability theory and statistics, Stochastic processes, Signal processing and data analysis. data IA

Bibliography

Aymard P, Boffi J-C, Asari H, Prevedel R, Holcman D (2025). Column-Like Subnetwork Reconstruction in Motor Cortex from Graph-Based 3D High-Density Two-Photon Calcium Imaging. bioRxiv 2025.06.17.660119.
Zonca L, Bellier FC, Milior G, Aymard P, Visser J, Rancillac A, Rouach N, Holcman D (2025). Unveiling the functional connectivity of astrocytic networks with AstroNet. Communications Biology 8:114.
David F, Sun C, Michel P-O, Sibille J, Rouach N, Holcman D (2025). Thalamocortical coupling and cortical E–I balance generate diverse anesthetic α-spindles for interpretable EEG decoding. bioRxiv 2025.12.25.696413.
Cartailler J, Parutto P, Touchard C, Vallée F, Holcman D (2019). Alpha rhythm collapse predicts iso-electric suppressions during anesthesia. Communications Biology 2:327.
Gavish M, Donoho DL (2014). The Optimal Hard Threshold for Singular Values is 4/√3. IEEE Transactions on Information Theory 60(8):5040-5053.
Foi A, Trimeche M, Katkovnik V, Egiazarian K (2008). Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-Image Raw-Data. IEEE Transactions on Image Processing 17(10):1737-1754.

Keywords

signal, denoising, neuronal network, extreme state, graph, astrocytes