Minimal Data Fidelity for Stellar Feature and Companion Detection

Technological advances in instrumentation have led to an exponential increase in exoplanet detection and scrutiny of stellar features such as spots and faculae. While the spots and faculae enable us to understand the stellar dynamics, exoplanets provide us with a glimpse into stellar evolution. While the ubiquity of noise (e.g., telluric, instrumental, or photonic) is unavoidable, combining this with increased spectrographic resolution compounds technological challenges. To account for these noise sources and resolution issues, we use a temporal multifractal framework to study data from the Spot Oscillation And Planet 2.0 tool, which simulates a stellar spectrum in the presence of a spot, a facula or a planet. Given these controlled simulations, we vary the resolution as well as the signal-to-noise ratio (S/N) to obtain a lower limit on the resolution and S/N required to robustly detect features. We show that a spot and a facula with a 1% coverage of the stellar disk can be robustly detected for a S/N (per pixel) of 35 and 60, respectively, for any spectral resolution above 20,000, while a planet with a radial velocity of 10 m s−1 can be detected for a S/N (per pixel) of 600. Rather than viewing noise as an impediment, our approach uses noise as a source of information.

IPGM: Inertial Proximal Gradient Method for Convolutional Dictionary Learning

Inspired by the recent success of the proximal gradient method (PGM) and recent efforts to develop an inertial algorithm, we propose an inertial PGM (IPGM) for convolutional dictionary learning (CDL) by jointly optimizing both an ℓ2-norm data fidelity term and a sparsity term that enforces an ℓ1 penalty. Contrary to other CDL methods, in the proposed approach, the dictionary and needles are updated with an inertial force by the PGM. We obtain a novel derivative formula for the needles and dictionary with respect to the data fidelity term. At the same time, a gradient descent step is designed to add an inertial term. The proximal operation uses the thresholding operation for needles and projects the dictionary to a unit-norm sphere. We prove the convergence property of the proposed IPGM algorithm in a backtracking case. Simulation results show that the proposed IPGM achieves better performance than the PGM and slice-based methods that possess the same structure and are optimized using the alternating-direction method of multipliers (ADMM).

Generalized deep iterative reconstruction for sparse-view CT imaging

Sparse-view CT is a promising approach in reducing the X-ray radiation dose in clinical CT imaging. However, the CT images reconstructed from the conventional filtered backprojection (FBP) algorithm suffer from severe streaking artifacts. Iterative reconstruction (IR) algorithms have been widely adopted to mitigate these streaking artifacts, but they may prolong the CT imaging time due to the intense data-specific computations. Recently, model-driven deep learning (DL) CT image reconstruction method, which unrolls the iterative optimization procedures into the deep neural network, has shown exciting prospect in improving the image quality and shortening the reconstruction time. In this work, we explore the generalized unrolling scheme for such iterative model to further enhance its performance on sparse-view CT imaging. By using it, the iteration parameters, regularizer term, data-fidelity term and even the mathematical operations are all assumed to be learned and optimized via the network training. Results from the numerical and experimental sparse-view CT imaging demonstrate that the newly proposed network with the maximum generalization provides the best reconstruction performance.

Inverse Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks

We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.