Young Investigators Lecture
ABSTRACT: This talk focuses on representations and algorithms for visual data, in light of recent theoretical and algorithmic developments in high-dimensional data analysis. We first consider the problem of modeling a given dataset as superpositions of basic motifs. This simple model arises from several important applications, including microscopy image analysis, neural spike sorting and image deblurring. This motif-finding problem can be phrased as '"short-and-sparse" blind deconvolution, in which the goal is to recover a short motif (convolution kernel) from its convolution with a random spike train. We assume the kernel to have unit Frobenius norm, and formulate it as a nonconvex optimization problem over the sphere. By analyzing the optimization landscape, we argue that when the target spike train is sufficiently sparse, then on a region of the sphere, every local minimum is equivalent to the ground truth. This geometric characterization implies that efficient methods obtain the ground truth under the same conditions. We next consider the problem of modeling physical nuisances across a collection of images, in the context of illumination-invariant object detection and recognition. We study the image formation process for general nonconvex objects (faces etc.), and propose a test data construction methodology that achieves object verification with worst-case performance guarantees. In addition, we leverage tools from sparse and low-rank decomposition to reduce the complexity for both storage and computation. These examples show the possibility of formalizing certain vision problems with rigorous guarantees.
BIO: Yuqian Zhang is a Ph.D. candidate in the Electrical Engineering Department at Columbia University and is advised by Professor John Wright. She received her B.S. in Electrical Engineering from Xi'an Jiaotong University. She was selected to participate in the Rising Stars in EECS Workshop 2017. Her research spans across optimization, computer vision, signal processing, and machine learning. Specifically, her primary research interest is to develop efficient, reliable and robust algorithms for applications in computer vision, scientific data analysis, etc.