Learning-based Wavelet-like Transforms For Fully Scalable and Accessible Image Compression

The goal of this thesis is to improve the existing wavelet transform with the aid of machine learning techniques, so as to enhance coding efficiency of wavelet-based image compression frameworks, such as JPEG 2000. In this thesis, we first propose to augment the conventional base wavelet transform with two additional learned lifting steps -- a high-to-low step followed by a low-to-high step. The high-to-low step suppresses aliasing in the low-pass band by using the detail bands at the same resolution, while the low-to-high step aims to further remove redundancy from detail bands by using the corresponding low-pass band. These two additional steps reduce redundancy (notably aliasing information) amongst the wavelet subbands, and also improve the visual quality of reconstructed images at reduced resolutions. To train these two networks in an end-to-end fashion, we develop a backward annealing approach to overcome the non-differentiability of the quantization and cost functions during back-propagation. Importantly, the two additional networks share a common architecture, named a proposal-opacity topology, which is inspired and guided by a specific theoretical argument related to geometric flow. This particular network topology is compact and with limited non-linearities, allowing a fully scalable system; one pair of trained network parameters are applied for all levels of decomposition and for all bit-rates of interest. By employing the additional lifting networks within the JPEG2000 image coding standard, we can achieve up to 17.4% average BD bit-rate saving over a wide range of bit-rates, while retaining the quality and resolution scalability features of JPEG2000. Built upon the success of the high-to-low and low-to-high steps, we then study more broadly the extension of neural networks to all lifting steps that correspond to the base wavelet transform. The purpose of this comprehensive study is to understand what is the most effective way to develop learned wavelet-like transforms for highly scalable and accessible image compression. Specifically, we examine the impact of the number of learned lifting steps, the number of layers and the number of channels in each learned lifting network, and kernel support in each layer. To facilitate the study, we develop a generic training methodology that is simultaneously appropriate to all lifting structures considered. Experimental results ultimately suggest that to improve the existing wavelet transform, it is more profitable to augment a larger wavelet transform with more diverse high-to-low and low-to-high steps, rather than developing deep fully learned lifting structures

A clear view of the primordial Universe

Observations of temperature anisotropies in the cosmic microwave background (CMB) and measurements of the large-scale structure of matter have established the standard Lambda cold dark matter model of cosmology. Precise measurements of new observables will test extensions to the standard cosmological model, e.g., a non-zero tensor-to-scalar ratio of primordial perturbations, a running of the spectral index of the primordial power spectrum (both tests of cosmic inflation), or new components like massive neutrinos and warm dark matter (WDM). Two of the most promising observables to test these extensions in upcoming surveys are polarisation anisotropies in the CMB and correlations in the Lyman-alpha forest. Accurate cosmological parameter estimation, however, is only achievable through careful consideration of instrumental and astrophysical systematic effects, either by removing contamination in data or modelling its effect during statistical inference. I present new approaches to controlling contaminants to CMB temperature and polarisation and the Lyman-alpha forest. The primary contamination to the CMB is foreground Galactic radiation, e.g., synchrotron and thermal dust emission. I demonstrate the use of directional wavelets in more accurately reconstructing CMB temperature maps in the presence of these foregrounds, using Planck simulations and data. The complexity of polarised Galactic emissions limits constraints on inflation and neutrinos using CMB polarisation. I show how spin directional wavelets can allow additional morphological information to improve cosmic and foreground component separation. The Lyman-alpha forest probes the primordial power spectrum and the suppression of small-scale clustering by neutrinos or WDM. However, estimation of the shape of the power spectrum is biased by broadened absorption lines formed by high density systems of neutral hydrogen. I present models of their effect, built from Illustris cosmological hydrodynamical simulations. Being functions of absorber column density provides the flexibility to model residual contamination, after the largest absorbers have been removed from data