Overcomplete Dictionary and Deep Learning Approaches to Image and Video Analysis

Extracting useful information while ignoring others (e.g. noise, occlusion, lighting) is an essential and challenging data analyzing step for many computer vision tasks such as facial recognition, scene reconstruction, event detection, image restoration, etc. Data analyzing of those tasks can be formulated as a form of matrix decomposition or factorization to separate useful and/or fill in missing information based on sparsity and/or low-rankness of the data. There has been an increasing number of non-convex approaches including conventional matrix norm optimizing and emerging deep learning models. However, it is hard to optimize the ideal l0-norm or learn the deep models directly and efficiently. Motivated from this challenging process, this thesis proposes two sets of approaches: conventional and deep learning based. For conventional approaches, this thesis proposes a novel online non-convex lp-norm based Robust PCA (OLP-RPCA) approach for matrix decomposition, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. A robust face recognition framework is also developed from Robust PCA and sparse coding approaches. More importantly, OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples. The proposed OLP-RPCA and LP-RPCA approaches are evaluated in various applications including Gaussian/non-Gaussian image denoising, face modeling, real-time background subtraction and video inpainting and compared against numerous state-of-the-art methods to demonstrate the robustness of the algorithms. In addition, this thesis proposes a novel Robust lp-norm Singular Value Decomposition (RP-SVD) method for analyzing two-way functional data. The proposed RP-SVD is formulated as an lp-norm based penalized loss minimization problem. The proposed RP-SVD method is evaluated in four applications, i.e. noise and outlier removal, estimation of missing values, structure from motion reconstruction and facial image reconstruction. For deep learning based approaches, this thesis explores the idea of matrix decomposition via Robust Deep Boltzmann Machines (RDBM), an alternative form of Robust Boltzmann Machines, which aiming at dealing with noise and occlusion for face-related applications, particularly. This thesis proposes an extension to texture modeling in the Deep Appearance Models (DAMs) by using RDBM to enhance its robustness against noise and occlusion. The extended model can cope with occlusion and extreme poses when modeling human faces in 2D image reconstruction. This thesis also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities

Improvements to the limb scattering stratospheric aerosol record

In the last decade stratospheric aerosols have gained considerable attention due to the influence of a series of moderate volcanic eruptions. The eruptions have been explosive enough to inject aerosols and precursors into the stratosphere and cause minor but important radiative and chemical effects, impacting projections and modelling of the global climate. Improved understanding of these effects requires accurate measurements of aerosol levels at spatial and temporal scales that resolve the rapidly changing conditions after events such as volcanic eruptions while also providing global information. This has been enabled by the advent of satellite profiling observations beginning in the 1980s that are able to produce global, vertically resolved measurements of stratospheric aerosols. These records have helped improve estimates of radiative forcing but remain uncertain in key aspects, including the magnitude of the biases between different measurement systems, errors in records due to retrieval assumptions, and aerosol levels in the upper troposphere and lower stratosphere. This work quantifies and addresses these limitations using three studies. First, biases are explored between the two longest satellite-based stratospheric aerosol records: SAGE II from 1984-2005 and OSIRIS from 2001-present. Biases are found to be relatively small, approximately 10\%, in the majority of the stratosphere, and a merged aerosol record spanning 35 years is produced by adjusting for these measurement biases. This work produced an aerosol climatology suitable for use in climate models, but did not determine the reasons for the biases. The second study compares two instruments and their retrievals, OSIRIS and SCIAMACHY, to investigate the major sources of error. It is found that errors in the a priori assumptions including particle size and the aerosol profile at high altitudes cause the majority of biases, while differences in the retrieval techniques and the radiative transfer models have mostly negligible impacts. The final study uses these results to develop a new multi-wavelength retrieval for OSIRIS measurements that aims to minimize the errors from a priori assumptions and improve retrieval sensitivity in the upper troposphere and lower stratosphere. This is used to produce the publicly available version 7 OSIRIS aerosol product, and is validated using comparisons with SAGE measurements as well as satellite lidar observations. Significant reductions in particle size biases are found with this new algorithm, and an updated cloud filter allows for retrievals at lower altitudes than previously possible

Nucleon-nucleon scattering process in Lattice Chiral Effective Field Theory approach up to next-to-next-to-next-to-leading order

We carry out a comprehensive analysis of the neutron-proton interaction up to the third order in the scheme of chiral effective field theory on the lattice. The complete two-pion exchange potential is taken into account to allow for a variation of the lattice spacing. We analyze the perturbative as well as the non-perturbative inclusion of the higher-order corrections and present a thorough analysis of the theoretical uncertainties. In addition, a first attempt is made to include chiral contributions at the fourth order as well as the electromagnetic effects relevant for proton-proton scattering. For that, we include all fourth order local four-nucleon interactions and the dominant corrections to the two-pion exchanges. As expected, the higher order chiral corrections give an improved description for the scattering of two nucleons. This work should be extended by performing an uncertainty analysis and investigating the lattice spacing dependence in the future. We further scrutinize nuclei with even and equal numbers of protons and neutrons using nuclear lattice effective field theory, based upon a set of highly improved (smeared) leading order interactions. We present numerical evidence that reveals a first-order transition at zero temperature from a Bose-condensed gas of alpha particles to the nuclear liquid, which is regulated by the strength and locality of the nucleon-nucleon interactions