💻 computer science

Bayesian In Vivo Tracking of Synapses using Joint Poisson Deconvolution and Diffeomorphic Registration

This paper presents a novel unified Bayesian framework that simultaneously performs image denoising, deconvolution, intensity inference, and diffeomorphic registration to robustly track and model the dynamic reorganization of synapses in noisy, motion-corrupted longitudinal *in vivo* two-photon microscopy data.

Original authors: Shashwat Kumar, Dominic M. Padova, Binish Narang, Gabrielle I. Coste, Austin R. Graves, Richard L. Huganir, Adam S. Charles, Michael I. Miller, Anuj Srivastava

Published 2026-05-14

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CC BY 4.0

Original authors: Shashwat Kumar, Dominic M. Padova, Binish Narang, Gabrielle I. Coste, Austin R. Graves, Richard L. Huganir, Adam S. Charles, Michael I. Miller, Anuj Srivastava

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to watch a busy, crowded dance floor through a foggy window at night. The dancers (synapses) are tiny, glowing dots. They are moving around, sometimes bumping into each other, and the window is blurry. To make things worse, the camera you are using is very sensitive to light, so the image is full of static (noise), and the dancers themselves are flickering unpredictably.

This is the challenge scientists face when trying to track synapses—the tiny connection points between brain cells—inside a living animal over several days.

This paper introduces a new, smarter way to solve this puzzle. Instead of trying to clean up the picture first and then count the dancers, the authors built a "virtual reality" simulation that tries to guess what the dance floor actually looks like, and then checks if their guess matches the blurry, noisy photo they took.

Here is how their method works, broken down into simple concepts:

1. The Old Way vs. The New Way

The Old Way (The "Clean-then-Count" Pipeline):
Imagine trying to fix the photo by first running it through a filter to remove the static (denoising). The problem is, this filter often smears the dancers together. If two dancers are close, the filter blurs them into one big blob. Then, you try to count the blobs. If you missed a dancer or merged two into one, your count is wrong, and you can't fix it later because the original data is gone.

The New Way (The "Bayesian Detective"):
The authors act like a detective who doesn't just look at the photo, but builds a story. They say: "Let's imagine there are X glowing dots moving in a specific way. Let's simulate what the photo would look like if that were true, including the blur and the static. Then, let's compare our simulation to the real photo. If they don't match, we tweak our story and try again."

They repeat this process millions of times until they find the story (the positions and movements of the dots) that best explains the messy photo.

2. The Three Magic Ingredients

To make this story work, they combined three specific ideas:

The "Ghost" Dancers (Point Sources): They assume the synapses are just tiny, glowing points of light. They don't try to guess the shape of the dancer, just their location and brightness.
The "Rubber Sheet" (Diffeomorphic Registration): Tissue in a living brain isn't rigid; it stretches and squishes like a rubber sheet. If you move your head, the brain moves with it. The authors use a mathematical "rubber sheet" model to figure out how the tissue warped between today's photo and yesterday's. This ensures that a dancer who moved slightly to the left is still recognized as the same dancer, not a new one.
The "Starlight" Math (Poisson Statistics): In low-light photography, light doesn't arrive smoothly; it arrives in random packets (like raindrops hitting a roof). The authors use a specific math model (Poisson) that understands this randomness. This helps them distinguish between a real dancer and a random burst of static noise.

3. What They Actually Found

The paper tested this method in two ways:

Fake Data (Simulation): They created a computer-generated movie of glowing dots moving through a blurry, noisy world. Their method successfully figured out exactly where the dots were and how they moved, even when the dots were very close together or the noise was heavy.
Real Data (Mouse Brain): They used real images from a mouse brain over two weeks.
- The Result: Their method produced a much clearer picture of the synapses than previous methods.
- The Key Win: Because they modeled the movement of the tissue, the "dancers" stayed consistent. In previous methods, a synapse might disappear one day and reappear in a different spot the next, or two synapses might merge into one. The new method kept the identities of the synapses stable, even when they were crowded together.

4. The "Uncertainty" Bonus

One of the coolest features of this method is that it doesn't just give you an answer; it tells you how sure it is. It's like a weather forecast that says, "It will rain," versus "It will rain, but I'm only 60% sure." The authors can show you a "confidence region" around every synapse, telling you exactly how blurry or uncertain that specific measurement is.

Summary

In short, this paper presents a new tool that treats brain imaging like a complex puzzle. Instead of trying to clean the image first, it builds a mathematical model of how the brain moves and how light behaves, then uses that model to reconstruct the true positions of synapses from the noisy, blurry data. This allows scientists to track the same tiny brain connections over weeks, even when the tissue shifts and the images are grainy.

Limitations mentioned in the paper:
The authors note that this method is computationally expensive (it takes a lot of computer power and time to run). Also, if the synapses are packed extremely tightly together (like a crowd of people shoulder-to-shoulder), it becomes mathematically difficult to tell them apart, just as it is hard to distinguish individual people in a dense crowd even with a perfect camera.

Technical Summary: Bayesian In Vivo Tracking of Synapses using Joint Poisson Deconvolution and Diffeomorphic Registration

Problem Statement

Longitudinal in vivo imaging of fluorescently tagged synaptic receptors offers a pathway to study large-scale synaptic dynamics and their disruption in neurological diseases. However, extracting reliable data from 2-photon microscopy faces significant challenges:

Low Signal-to-Noise Ratio (SNR): To prevent photobleaching, low laser power is used, resulting in high shot noise and Poisson-distributed photon counts.
Nonlinear Tissue Motion: Synapses move with dendritic branches and surrounding tissue between imaging sessions, causing complex, non-rigid deformations.
Optical Blur: The microscope Point Spread Function (PSF) induces significant blur, which is exacerbated in regions of high synaptic density.
Pipeline Limitations: Existing "denoise-segment-track" pipelines (e.g., using autoencoders followed by CNN-based detection) often fail in crowded or low-SNR regimes. Denoising can blur adjacent synapses, causing segmentation networks to merge distinct sources. Furthermore, these pipelines discard uncertainty information and make local decisions that can bias fluorescence estimates and fail to model nonlinear deformation explicitly.

Methodology

The authors propose a unified Bayesian framework that treats synapse tracking as a joint inference problem, moving away from sequential processing steps. The core of the method is a generative model that synthesizes observed images from latent variables.

1. Mathematical Formulation

The model represents synapses as a dynamic catalogue of point sources evolving under a smooth, topology-preserving deformation field.

Synapse Representation: Synapses are modeled as a singular density $\mu_t(x) = \sum f_{i,t} \delta(x - x_i)$ , where $x_i$ are locations and $f_{i,t}$ are fluorescence intensities.
Diffeomorphic Deformation: Nonlinear tissue motion is modeled via diffeomorphisms $\phi_t: D \to D$ . To parameterize this efficiently, the authors use generalized momenta ( $p_{i,t}$ ) in a reproducing kernel Hilbert space. The displacement field is approximated as $\phi_t(x) \approx x + u_t(x)$ , where $u_t$ is a linear combination of kernel functions weighted by momenta. This ensures smooth, invertible transformations that preserve topology.
Image Formation: The expected image intensity $\lambda_t(x)$ is the convolution of the deformed synapse density with a Gaussian Point Spread Function (PSF), plus a background intensity $\lambda_0$ .
Observation Model: The raw photon counts $N_t(x)$ are modeled as Poisson random variables with mean $\lambda_t(x) + \lambda_0$ .

2. Bayesian Inference

The goal is to infer the joint posterior distribution of all unknown parameters $\theta = \{x_i, f_{i,t}, p_{i,t}, \lambda_0\}$ given the observed photon counts.

Priors:
- Synapse locations: Uniform distribution over the domain.
- Fluorescence: Independent exponential distribution (encouraging sparsity).
- Momenta: Independent Gaussian distribution (inducing smooth deformations).
- Background: Half-normal distribution.
Inference Algorithm: Due to the complexity of the posterior (nonlinear deformations and convolutions), the authors employ Hamiltonian Monte Carlo (HMC), specifically the No-U-Turn Sampler (NUTS) implemented in PyMC. This allows for sampling from the posterior to estimate parameter distributions and provide calibrated uncertainty estimates.

Key Contributions

Tracking-by-Synthesis with Diffeomorphic Templates: Instead of detecting and linking discrete objects, the method fits a latent catalogue of point sources that "wiggle" under diffeomorphic transformations. This synthesizes virtual synapses that provide temporally coherent explanations of longitudinal images, implicitly handling tracking without separate association steps.
Physics-Based Generative Model: The model explicitly incorporates imaging physics, including a parameterized Gaussian PSF and Poisson statistics for both foreground signal and background shot noise, rather than relying on heuristic denoising.
Joint Bayesian Inference with Uncertainty: The framework simultaneously performs image registration (correcting tissue motion), constructs the synapse catalogue, denoises data, and infers fluorescence intensities. Crucially, it provides calibrated uncertainty estimates for all parameters, avoiding the error propagation common in sequential pipelines.

Experimental Results

The framework was evaluated on both simulated data and real in vivo datasets from a SEP-GluA2 transgenic mouse line (imaged over two weeks).

Simulated Data

Performance: The model successfully recovered ground-truth synapse locations, fluorescence intensities, and deformation fields despite substantial blur and shot noise.
Temporal Coupling: Increasing the number of time points ( $T$ ) improved template localization and reduced ambiguity, demonstrating the benefit of temporal constraints.
Density Limitations: Performance degraded as synapse density increased due to overlapping PSFs, highlighting a fundamental identifiability limit in the imaging model.

Real In Vivo Data

Comparison: The method was compared against a denoising autoencoder (XTC), Non-Local Means (NLM), and BM3D.
Metrics:
- Poisson Log-Likelihood: The Bayesian model achieved significantly higher likelihood (-3.62) compared to XTC (-16.13), indicating a better fit to the raw photon statistics.
- Temporal Consistency: The model showed superior temporal stability (Pearson correlation of 0.577 vs. 0.387 for XTC), maintaining coherent synapse identities across days.
- Peak Stability: The number of detected peaks remained stable across frames (std 0.97), whereas baselines showed high variability (e.g., XTC std 1.92).
Qualitative Results: Unlike the autoencoder, which produced visually similar but temporally inconsistent intensities, the Bayesian model maintained consistent synapse identities. The inferred displacement fields were smooth and free of self-intersections, preventing biologically implausible motions like folding.

Significance and Claims

The paper claims that by unifying image formation, motion modeling, and noise statistics into a single probabilistic inverse model, the proposed framework overcomes the limitations of current "denoise-segment-track" pipelines.

Robustness: It handles low-SNR and nonlinear deformation conditions more effectively by leveraging the physical constraints of the microscope and the temporal structure of the data.
Coherence: Tracking emerges naturally from the generative model, ensuring that synapse identities remain consistent over time without requiring explicit data association algorithms that are prone to merge/split errors in crowded regions.
Uncertainty Quantification: The method provides a principled way to estimate confidence in synapse locations and intensities, which is critical for analyzing subtle biological changes.

The authors acknowledge that the current approach is computationally expensive due to MCMC inference and that recovery remains challenging in extremely dense synaptic regimes. Future work aims to improve PSF approximation and explore more efficient inference methods to scale to larger brain volumes.