Learning Convolutional Sparse Representations

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering


PhD Thesis Defence


Title: "Learning Convolutional Sparse Representations"

By

Miss Yaqing WANG


Abstract

Learning sparse representations by sparse coding has been used in many 
applications for decades. Recently, convolutional sparse coding (CSC) improves 
sparse coding by learning a shift-invariant dictionary and convolutional sparse 
representations from the data. It has been successfully extracting local 
patterns from various data types, such as trajectories, images, audios, videos, 
multi-spectral and light field images, and biomedical data. However, most 
existing CSC algorithms operate in the batch mode and are computationally 
expensive. This lack of scalability restricts the use of CSC on large-scale 
data. Apart from that, existing CSC works mainly assume that the noise in the 
data is from Gaussian distribution, which can be restrictive and does not suit 
many real-world problems. In this thesis, we first propose a scalable online 
CSC algorithm called OCSC for data sets of large quantity. The key is a 
reformulation of the CSC objective so that convolution can be handled easily in 
the frequency domain, and much smaller space is needed. Empirical results 
validate that OCSC is more scalable, has faster convergence and better 
reconstruction performance. Further, instead of convolving with a dictionary 
shared by all samples, we propose the use of a sample-dependent dictionary in 
which each filter is a linear combination of a small set of base filters 
learned from data. This added flexibility allows a large number of 
sample-dependent patterns to be captured, which is especially useful in the 
handling of large or high-dimensional data sets. Computationally, the resultant 
model can be efficiently learned by online learning. Finally, we propose a 
general CSC model capable of learning convolutional filters and representations 
from data with complicated unknown noise. The noise is now modeled by Gaussian 
mixture model, which can approximate any continuous probability density 
function. We use the expectation-maximization algorithm to solve the problem 
and design an efficient method for the weighted CSC problem in the maximization 
step. The crux is to speed up the convolution in the frequency domain while 
keeping the other computation involving weight matrix in the spatial domain. We 
show that this method obtains comparable time and space complexity compared 
with existing CSC methods, models noise effectively and obtains high-quality 
filters and representation. In sum, we propose a series of works to make CSC 
scalable to deal with large data, capable of extracting a large number of local 
patterns, and free of contamination of complicated noises. Therefore, better 
representations and dictionary can be obtained.


Date:			Friday, 5 July 2019

Time:			2:00pm - 4:00pm

Venue:			Room 3494
 			Lifts 25/26

Chairman:		Prof. Xijun Hu (CBE)

Committee Members:	Prof. Lionel Ni (Supervisor)
 			Prof. James Kwok (Supervisor)
 			Prof. Qifeng Chen
 			Prof. Cunsheng Ding
 			Prof. Ping Gao (CBE)
 			Prof. Song Gao (PolyU)


**** ALL are Welcome ****