In this talk I discuss correlation imaging in the context of adaptive optics in next generation telescope imaging. Moreover, I discuss the connections to covariance estimation in statistics.
The recent discovery of inertial waves on the surface of the Sun offers new possibilities to learn about the solar interior. These waves are long-lived with a period on the order of the Sun rotation period (~27 days) and are sensitive to parameters deep inside the Sun. They are excited by turbulent convection, leading to a passive imaging problem. In this work, we present the forward and...
A major problem within the field of aeroacoustics is determining the distribution of an aeroacoustic source, such as an airplane engine, given pressure measurements on external microphone arrays. Taking a Bayesian view and modeling the source as fundamentally random with zero mean leads to the problem of determining the covariance of the random source.
While this can be recovered from...
We address the computational efficiency of the A-optimal Bayesian design of experiments . A-optimality is a widely used criterion in Bayesian experiment design, aiming to minimize the expected conditional variance and find the optimal design. We propose a novel likelihood-free method for the A-optimal experiment design that does not require sampling or approximating the Bayesian posterior...
Many inverse problems in science and engineering are often subject to uncertainty, especially when the measurement data is complex and indirect. To reduce uncertainty, one needs to find a way to measure the data efficiently. This problem falls under the umbrella of the optimal experimental design (OED). The computational cost of OED, however, is notoriously expensive, so in practice, one...
Semiconductor devices such as nano-biosensors have many applications in our real life including medical applications for diagnostic purposes. In this work, we describe incorporating uncertainties in the mathematical modeling of semiconductor devices, as well as the propagation of uncertainties in the solution of the corresponding PDE model. We then formulate and solve a Bayesian inverse...
Photoacoustic tomography (PAT) is a rapidly evolving imaging technique that combines the high contrast of optical imaging with the high resolution of ultrasound imaging. When dealing with typically noisy measurement data, one aims to identify certain parameters in the governing PDEs for the photoacoustic tomography system. Therefore, an essential factor in estimating these parameters is the...
In inverse problems, one often assumes a model for how the data is generated from the underlying parameter of interest. In experimental design, the goal is to choose observations to reduce uncertainty in the parameter. When the true model is unknown or expensive, an approximate model is used that has nonzero `model error' with respect to the true data-generating model. Model error can lead to...
We present an approach for optimal experimental design (OED) for Bayesian inverse problems characterized by non-Gaussian, intractable posteriors. Our transport-map-based approach is versatile, accommodating various optimality criteria, design types, and prior distributions. In this talk, we highlight the key aspects of our method with a focus on the Bayesian D-optimality criterion, which aims...
Bayesian optimal experimental design (OED) seeks to maximize the expected information gain for the reconstruction of unknown quantities in an experiment by optimizing the placement of measurements. The objective function in the resulting optimization problem contains a high-dimensional integral with respect to the posterior distribution. We will approximate these high-dimensional integrals...
Measuring the expected information gain (EIG) of an experiment allows for comprehensive design optimization. Efficiently estimating the EIG is crucial when data are scarce or costly to obtain. We propose several estimators combining the randomized quasi-Monte Carlo method with Laplace-based importance sampling, and showcase their efficiency both theoretically and via numerical examples.
The recent discovery of rotation-induced inertial waves on the surface of the Sun [1] promises to open a new branch of helio- and asteroseismology. Solar inertial wave observations, combined with linear eigenvalue analysis, can help us probe the internal rotation of the Sun, as well as the thermal structure of its convective envelope [2,3]. However, since inertial modes are stochastically...
