Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications

Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections

Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model

Light microscopy is a widespread and inexpensive imaging technique facilitating biomedical discovery and diagnostics. However, light diffraction barrier and imperfections in optics limit the level of detail of the acquired images. The details lost can be reconstructed among others by deep learning models. Yet, deep learning models are prone to introduce artefacts and hallucinations into the reconstruction. Recent state-of-the-art image synthesis models like the denoising diffusion probabilistic models (DDPMs) are no exception to this. We propose to address this by incorporating the physical problem of microscopy image formation into the model's loss function. To overcome the lack of microscopy data, we train this model with synthetic data. We simulate the effects of the microscope optics through the theoretical point spread function and varying the noise levels to obtain synthetic data. Furthermore, we incorporate the physical model of a light microscope into the reverse process of a conditioned DDPM proposing a physics-informed DDPM (PI-DDPM). We show consistent improvement and artefact reductions when compared to model-based methods, deep-learning regression methods and regular conditioned DDPMs.Comment: 16 pages, 5 figure

Contributions To Automatic Particle Identification In Electron Micrographs: Algorithms, Implementation, And Applications

Three dimensional reconstruction of large macromolecules like viruses at resolutions below 8 Ã… - 10 Ã… requires a large set of projection images and the particle identification step becomes a bottleneck. Several automatic and semi-automatic particle detection algorithms have been developed along the years. We present a general technique designed to automatically identify the projection images of particles. The method utilizes Markov random field modelling of the projected images and involves a preprocessing of electron micrographs followed by image segmentation and post processing for boxing of the particle projections. Due to the typically extensive computational requirements for extracting hundreds of thousands of particle projections, parallel processing becomes essential. We present parallel algorithms and load balancing schemes for our algorithms. The lack of a standard benchmark for relative performance analysis of particle identification algorithms has prompted us to develop a benchmark suite. Further, we present a collection of metrics for the relative performance analysis of particle identification algorithms on the micrograph images in the suite, and discuss the design of the benchmark suite