Robust Algorithms for Low-Rank and Sparse Matrix Models

Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them. This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd

PS-FCN: A Flexible Learning Framework for Photometric Stereo

This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not require a pre-defined set of light directions during training and testing, and can handle multiple images and light directions in an order-agnostic manner. Although we train PS-FCN on synthetic data, it can generalize well on real datasets. We further show that PS-FCN can be easily extended to handle the problem of uncalibrated photometric stereo.Extensive experiments on public real datasets show that PS-FCN outperforms existing approaches in calibrated photometric stereo, and promising results are achieved in uncalibrated scenario, clearly demonstrating its effectiveness.Comment: ECCV 2018: https://guanyingc.github.io/PS-FC

Photo-Realistic Facial Details Synthesis from Single Image

We present a single-image 3D face synthesis technique that can handle challenging facial expressions while recovering fine geometric details. Our technique employs expression analysis for proxy face geometry generation and combines supervised and unsupervised learning for facial detail synthesis. On proxy generation, we conduct emotion prediction to determine a new expression-informed proxy. On detail synthesis, we present a Deep Facial Detail Net (DFDN) based on Conditional Generative Adversarial Net (CGAN) that employs both geometry and appearance loss functions. For geometry, we capture 366 high-quality 3D scans from 122 different subjects under 3 facial expressions. For appearance, we use additional 20K in-the-wild face images and apply image-based rendering to accommodate lighting variations. Comprehensive experiments demonstrate that our framework can produce high-quality 3D faces with realistic details under challenging facial expressions