Point spread function modelling for astronomical telescopes: a review focused on weak gravitational lensing studies

The accurate modelling of the Point Spread Function (PSF) is of paramount importance in astronomical observations, as it allows for the correction of distortions and blurring caused by the telescope and atmosphere. PSF modelling is crucial for accurately measuring celestial objects' properties. The last decades brought us a steady increase in the power and complexity of astronomical telescopes and instruments. Upcoming galaxy surveys like Euclid and LSST will observe an unprecedented amount and quality of data. Modelling the PSF for these new facilities and surveys requires novel modelling techniques that can cope with the ever-tightening error requirements. The purpose of this review is three-fold. First, we introduce the optical background required for a more physically-motivated PSF modelling and propose an observational model that can be reused for future developments. Second, we provide an overview of the different physical contributors of the PSF, including the optic- and detector-level contributors and the atmosphere. We expect that the overview will help better understand the modelled effects. Third, we discuss the different methods for PSF modelling from the parametric and non-parametric families for ground- and space-based telescopes, with their advantages and limitations. Validation methods for PSF models are then addressed, with several metrics related to weak lensing studies discussed in detail. Finally, we explore current challenges and future directions in PSF modelling for astronomical telescopes.Comment: 63 pages, 14 figures. Submitte

Modelling Non-Equilibrium Molecular Formation and Dissociation for the Spectroscopic Analysis of Cool Stellar Atmospheres

Modelling techniques for stellar atmospheres are undergoing continuous improvement. In this thesis, I showcase how these methods are used for spectroscopic analysis and for modelling time-dependent molecular formation and dissociation. I first use CO5BOLD model atmospheres with the LINFOR3D spectrum synthesis code to determine the photospheric solar silicon abundance of 7.57 ± 0.04. This work also revealed some issues present in the cutting-edge methods, such as synthesised lines being overly broadened. Next, I constructed a chemical reaction network in order to model the time-dependent evolution of molecular species in (carbon-enhanced) metal-poor dwarf and red giant atmospheres, again using CO5 BOLD. This was to test if the assumption of chemical equi librium, widely assumed in spectroscopic studies, was still vaild in the photospheres of metal-poor stars. Indeed, the mean deviations from chemical equilibrium are below 0.2 dex across the spectroscopically relevant regions of the atmosphere, though deviations increase with height. Finally, I implemented machine learning methods in order to remove noise and line blends from spectra, as well as to predict the equilibrium state of a chemical reaction network. The methods used and developed in this thesis illustrate the importance of both conventional and machine learning modelling techniques, and merge them to further improve accuracy, precision, and efficiency

Automatic Object Detection and Categorisation in Deep Astronomical Imaging Surveys Using Unsupervised Machine Learning

I present an unsupervised machine learning technique that automatically segments and labels galaxies in astronomical imaging surveys using only pixel data. Distinct from previous unsupervised machine learning approaches used in astronomy the technique uses no pre-selection or pre-filtering of target galaxy type to identify galaxies that are similar. I demonstrate the technique on the Hubble Space Telescope (HST) Frontier Fields. By training the algorithm using galaxies from one field (Abell 2744) and applying the result to another (MACS0416.1-2403), I show how the algorithm can cleanly separate early and late type galaxies without any form of pre-directed training for what an ‘early’ or ‘late’ type galaxy is. I present the results of testing the technique for generalisation and to identify its optimal configuration. I then apply the technique to the HST Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) fields, creating a catalogue of 60000 labelled galaxies, grouped by their similarity. I show how the automatically identified groups contain galaxies with similar morphological (and photometric) type. I compare the catalogue to human-classifications from the Galaxy Zoo: CANDELS project. Although there is not a direct mapping, I demonstrate a good level of concordance between them. I publicly release the catalogue and a corresponding visual catalogue and galaxy similarity search facility at www.galaxyml.uk. I show how the technique can be used to identify rarer objects and present lensed galaxy candidates from the CANDELS imaging. Finally, I consider how the technique can be improved and applied to future surveys to identify transient objects

Advances in Image Processing, Analysis and Recognition Technology

For many decades, researchers have been trying to make computers’ analysis of images as effective as the system of human vision is. For this purpose, many algorithms and systems have previously been created. The whole process covers various stages, including image processing, representation and recognition. The results of this work can be applied to many computer-assisted areas of everyday life. They improve particular activities and provide handy tools, which are sometimes only for entertainment, but quite often, they significantly increase our safety. In fact, the practical implementation of image processing algorithms is particularly wide. Moreover, the rapid growth of computational complexity and computer efficiency has allowed for the development of more sophisticated and effective algorithms and tools. Although significant progress has been made so far, many issues still remain, resulting in the need for the development of novel approaches

The third 'CHiME' speech separation and recognition challenge: Analysis and outcomes

This paper presents the design and outcomes of the CHiME-3 challenge, the first open speech recognition evaluation designed to target the increasingly relevant multichannel, mobile-device speech recognition scenario. The paper serves two purposes. First, it provides a definitive reference for the challenge, including full descriptions of the task design, data capture and baseline systems along with a description and evaluation of the 26 systems that were submitted. The best systems re-engineered every stage of the baseline resulting in reductions in word error rate from 33.4% to as low as 5.8%. By comparing across systems, techniques that are essential for strong performance are identified. Second, the paper considers the problem of drawing conclusions from evaluations that use speech directly recorded in noisy environments. The degree of challenge presented by the resulting material is hard to control and hard to fully characterise. We attempt to dissect the various 'axes of difficulty' by correlating various estimated signal properties with typical system performance on a per session and per utterance basis. We find strong evidence of a dependence on signal-to-noise ratio and channel quality. Systems are less sensitive to variations in the degree of speaker motion. The paper concludes by discussing the outcomes of CHiME-3 in relation to the design of future mobile speech recognition evaluations

Audio computing in the wild: frameworks for big data and small computers

This dissertation presents some machine learning algorithms that are designed to process as much data as needed while spending the least possible amount of resources, such as time, energy, and memory. Examples of those applications, but not limited to, can be a large-scale multimedia information retrieval system where both queries and the items in the database are noisy signals; collaborative audio enhancement from hundreds of user-created clips of a music concert; an event detection system running in a small device that has to process various sensor signals in real time; a lightweight custom chipset for speech enhancement on hand-held devices; instant music analysis engine running on smartphone apps. In all those applications, efficient machine learning algorithms are supposed to achieve not only a good performance, but also a great resource-efficiency. We start from some efficient dictionary-based single-channel source separation algorithms. We can train this kind of source-specific dictionaries by using some matrix factorization or topic modeling, whose elements form a representative set of spectra for the particular source. During the test time, the system estimates the contribution of the participating dictionary items for an unknown mixture spectrum. In this way we can estimate the activation of each source separately, and then recover the source of interest by using that particular source's reconstruction. There are some efficiency issues during this procedure. First off, searching for the optimal dictionary size is time consuming. Although for some very common types of sources, e.g. English speech, we know the optimal rank of the model by trial and error, it is hard to know in advance as to what is the optimal number of dictionary elements for the unknown sources, which are usually modeled during the test time in the semi-supervised separation scenarios. On top of that, when it comes to the non-stationary unknown sources, we had better maintain a dictionary that adapts its size and contents to the change of the source's nature. In this online semi-supervised separation scenario, a mechanism that can efficiently learn the optimal rank is helpful. To this end, a deflation method is proposed for modeling this unknown source with a nonnegative dictionary whose size is optimal. Since it has to be done during the test time, the deflation method that incrementally adds up new dictionary items shows better efficiency than a corresponding na\"ive approach where we simply try a bunch of different models. We have another efficiency issue when we are to use a large dictionary for better separation. It has been known that considering the manifold of the training data can help enhance the performance for the separation. This is because of the symptom that the usual manifold-ignorant convex combination models, such as from low-rank matrix decomposition or topic modeling, tend to result in ambiguous regions in the source-specific subspace defined by the dictionary items as the bases. For example, in those ambiguous regions, the original data samples cannot reside. Although some source separation techniques that respect data manifold could increase the performance, they call for more memory and computational resources due to the fact that the models call for larger dictionaries and involve sparse coding during the test time. This limitation led the development of hashing-based encoding of the audio spectra, so that some computationally heavy routines, such as nearest neighbor searches for sparse coding, can be performed in a cheaper bit-wise fashion. Matching audio signals can be challenging as well, especially if the signals are noisy and the matching task involves a big amount of signals. If it is an information retrieval application, for example, the bigger size of the data leads to a longer response time. On top of that, if the signals are defective, we have to perform the enhancement or separation job in the first place before matching, or we might need a matching mechanism that is robust to all those different kinds of artifacts. Likewise, the noisy nature of signals can add an additional complexity to the system. In this dissertation we will also see some compact integer (and eventually binary) representations for those matching systems. One of the possible compact representations would be a hashing-based matching method, where we can employ a particular kind of hash functions to preserve the similarity among original signals in the hash code domain. We will see that a variant of Winner Take All hashing can provide Hamming distance from noise-robust binary features, and that matching using the hash codes works well for some keyword spotting tasks. From the fact that some landmark hashes (e.g. local maxima from non-maximum suppression on the magnitudes of a mel-scaled spectrogram) can also robustly represent the time-frequency domain signal efficiently, a matrix decomposition algorithm is also proposed to take those irregular sparse matrices as input. Based on the assumption that the number of landmarks is a lot smaller than the number of all the time-frequency coefficients, we can think of this matching algorithm efficient if it operates entirely on the landmark representation. On the contrary to the usual landmark matching schemes, where matching is defined rigorously, we see the audio matching problem as soft matching where we find a similar constellation of landmarks to the query. In order to perform this soft matching job, the landmark positions are smoothed by a fixed-width Gaussian caps, with which the matching job is reduced down to calculating the amount of overlaps in-between those Gaussians. The Gaussian-based density approximation is also useful when we perform decomposition on this landmark representation, because otherwise the landmarks are usually too sparse to perform an ordinary matrix factorization algorithm, which are originally for a dense input matrix. We also expand this concept to the matrix deconvolution problem as well, where we see the input landmark representation of a source as a two-dimensional convolution between a source pattern and its corresponding sparse activations. If there are more than one source, as a noisy signal, we can think of this problem as factor deconvolution where the mixture is the combination of all the source-specific convolutions. The dissertation also covers Collaborative Audio Enhancement (CAE) algorithms that aim to recover the dominant source at a sound scene (e.g. music signals of a concert rather than the noise from the crowd) from multiple low-quality recordings (e.g. Youtube video clips uploaded by the audience). CAE can be seen as crowdsourcing a recording job, which needs a substantial amount of denoising effort afterward, because the user-created recordings might have been contaminated with various artifacts. In the sense that the recordings are from not-synchronized heterogenous sensors, we can also think of CAE as big ad-hoc sensor array processing. In CAE, each recording is assumed to be uniquely corrupted by a specific frequency response of the microphone, an aggressive audio coding algorithm, interference, band-pass filtering, clipping, etc. To consolidate all these recordings and come up with an enhanced audio, Probabilistic Latent Component Sharing (PLCS) has been proposed as a method of simultaneous probabilistic topic modeling on synchronized input signals. In PLCS, some of the parameters are fixed to be same during and after the learning process to capture common audio content, while the rest of the parameters are for the unwanted recording-specific interference and artifacts. We can speed up PLCS by incorporating a hashing-based nearest neighbor search so that at every EM iteration PLCS can be applied only to a small number of recordings that are closest to the current source estimation. Experiments on a small simulated CAE setup shows that the proposed PLCS can improve the sound quality from variously contaminated recordings. The nearest neighbor search technique during PLCS provides sensible speed-up at larger scaled experiments (up to 1000 recordings). Finally, to describe an extremely optimized deep learning deployment system, Bitwise Neural Networks (BNN) will be also discussed. In the proposed BNN, all the input, hidden, and output nodes are binaries (+1 and -1), and so are all the weights and bias. Consequently, the operations on them during the test time are defined with Boolean algebra, too. BNNs are spatially and computationally efficient in implementations, since (a) we represent a real-valued sample or parameter with a bit (b) the multiplication and addition correspond to bitwise XNOR and bit-counting, respectively. Therefore, BNNs can be used to implement a deep learning system in a resource-constrained environment, so that we can deploy a deep learning system on small devices without using up the power, memory, CPU clocks, etc. The training procedure for BNNs is based on a straightforward extension of backpropagation, which is characterized by the use of the quantization noise injection scheme, and the initialization strategy that learns a weight-compressed real-valued network only for the initialization purpose. Some preliminary results on the MNIST dataset and speech denoising demonstrate that a straightforward extension of backpropagation can successfully train BNNs whose performance is comparable while necessitating vastly fewer computational resources

Cosmology with dark matter maps

Physics is experiencing an exciting period of exploration into the nature of dark energy, dark matter, and gravitation. With 95% of the mass-energy of the Universe still unexplained, the answers to many further fundamental questions of astro-, theoretical- and particle-physics are being hampered. In the coming years, DES, HSC, KiDS, Euclid and LSST will image billions of galaxies, aiming to use observational data from the late Universe to infer cosmological parameters and compare cosmological models. One of the most promising observables is the weak gravitational lensing effect. Using the statistical power from many small distortions, called shear, DES has provided excellent constraints. However, the standard 2-point statistics do not capture the full information in the data. In the late Universe, gravitational collapse has led to a highly non-Gaussian density field, for which 2-point correlations are not a unique statistical description, and even all N-point functions cannot completely characterize. The research presented in this thesis focuses on methods to reconstruct mass maps from DES weak lensing data and using map-based statistics to infer cosmological parameters and assess theoretical models in a principled Bayesian framework. In Chapter 2, I compare three mass mapping methods with closed-form priors using DES SV data and simulations. In Chapter 3, I demonstrate how the Wiener filter (one of the above methods) computation can be sped up by an order of magnitude using Dataflow Engines (reconfigurable hardware). In Chapter 4, I present a Bayesian hierarchical model which takes into account added uncertainty introduced when noisy simulations are used to generate theoretical predictions. In Chapter 5, with my publicly available DeepMass code, I demonstrate how mass maps reconstructions can be improved (> 10% mean-square-error compared with previously presented methods) using deep learning techniques trained on simulations. In Chapter 6, I discuss future work and the applicability of likelihood-free inference methods for map-based statistics