Systems | Information | Learning | Optimization

Poisson inverse and denoising problems in atmospheric lidar imaging & PULasso: High-dimensional variable selection with presence-only data

Willem’s Abstract:

Atmospheric light detection and ranging (lidar) provides a unique capability to resolve atmospheric vertical structures of clouds and aerosols with very high sensitivity at high altitude and temporal resolutions. A variety of lidar instruments exist which focus on the measurement of the optical properties of the atmosphere in order to study, for example, the radiative transfer of clouds and aerosols, and water-vapor density of the lower troposphere. A key challenge with all lidar instruments is the reduction of detector noise in order to increase the inference accuracy of atmospheric optical properties. Current lidar algorithms rely on high signal to noise ratio observations to accurately infer the required optical properties, which is achieved by either reducing the detector noise variance by image resolution reduction (summing over non-overlapping blocks of pixels) or employing two-dimensional lowpass filters.

New atmospheric lidar denoising and inversion methods are introduced in this talk which tie together atmospheric lidar modeling with previously developed Poisson denoising and inversion methods. We consider the denoising and reconstruction of very low intensity images corrupted by Poisson noise using a coarse-to-fine image resolution inference framework, which is easily generalizable to a variety of inverse problem settings. Specifically, the method is based on a regularized maximum likelihood formulation which is solved using a coarse-to-fine proximal gradient optimization algorithm and the regularization is enforced using the BM3D algorithm. We demonstrate that our proposed methods can deliver more accurate lidar inference results compared to the standard approach that is used by lidar experts.

Hyebin’s Abstract:
In various real-world problems, we are presented with positive and unlabelled data, also referred to as presence-only responses and where the number of covariates p is large. The combination of presence-only responses and high dimensionality presents both statistical and computational challenges. In this talk, I present the PUlasso algorithm for variable selection and classification with positive and unlabelled responses in the high dimensional setting. The algorithm uses the majorization-minimization (MM) framework, which is a generalization of the well-known expectation-maximization (EM) algorithm, and is equipped with two computational speed-ups for better scaling to large problems. We discuss algorithmic and theoretical guarantees of the proposed method and demonstrate its performance using beta-glucosidase enzyme sequence data.


January 24 @ 12:30
12:30 pm (1h)

Discovery Building, Orchard View Room

Hyebin Song, Willem Marais