Type: Master (semester project)
Supervisor: Vasiliki Stergiopoulou (LCAV, Galatea)
Contact: [email protected]
Project Context:
Third harmonic generation (THG) microscopy is a non-fluorescent multiphoton technique that enables three-dimensional imaging of refractive index differences. To obtain an accurate reconstruction, we tackle an optimization problem, minimizing a weighted combination of two terms. The first term ensures that reconstructions align well with measured data (data-fidelity term), while the second term favors a priori information for reconstruction. This project aims to study and refine the fidelity term, improving its alignment with the measurements and enhancing the effectiveness of the optimization problem.
Technical Insight:
THG measurements require a sophisticated approach to reconstruction, with a focus on refining the likelihood term – an essential factor in guaranteeing the fidelity of reconstructions. The initial task involves a comprehensive study of the CMOS camera’s sensor noise distribution, which encompasses among others photon noise, dark noise, and read noise.
Standard data fidelity terms, such as l2-squared norm or Kullback-Leibler divergence1, will be explored first. This exploration will be followed by the resolution of an optimization problem adapted to these terms. In cases where the initial noise model proves insufficient, the project will investigate learning the empirical noise distribution. Techniques such as Gaussian mixture models (GMMs) or other learning techniques will be employed for this purpose2.
The Python library pyxu3 will be used to implement the various schemes, taking advantage of its versatility and compatibility with scientific computing frameworks.
Objectives:
- Investigate noise distribution in THG measurements.
- Explore data-fidelity terms (standard ones from the literature or learnable ones).
- Solve an optimization problem for the various data-fidelity terms.
- Apply it to real-world microscopy data to validate its effectiveness.
Prerequisites:
- Background in signal processing.
- Programming skills in Python.
References:
1 J. Li, Z. Shen, R. Yin and X. Zhang, ” A reweighted l 2 method for image restoration with Poisson and mixed Poisson-Gaussian noise “, Inverse Probl. Imag, vol. 9, 2015.
2 J. Dong, et al., “Learning Data Terms for Non-blind Deblurring. In Computer Vision”, ECCV 2018.
3 https://pyxu-org.github.io/