This master’s thesis deals with the restoration of clipped multichannel audio signals based on sparse representations. First, a general theory of clipping and theory of sparse representations of audio signals is described. A short overview of existing restoration methods is part of this thesis as well. Subsequently, two declipping algorithms are introduced and are also implemented in the Matlab environment as a part of the thesis. The first one, SPADE, is considered a state- of-the-art method for mono audio signals declipping and the second one, CASCADE, which is derived from SPADE, is designed for the restoration of multichannel signals. In the last part of the thesis, both algorithms are tested and the results are compared using the objective measures SDR and PEAQ, and also using the subjective listening test MUSHRA.

This master’s thesis deals with the restoration of audio signals damaged by quantization. The theoretical part starts with a description of quantization and dequantization in general, few existing methods of dequantization of audio signals and theory of sparse representations of signals are also presented. The next part introduces algorithms suitable for dequantization, specifically Douglas–Rachford, Chambolle–Pock, SPADEQ and implementation of these algorithms in MATLAB application in the next chapter. In the last part of this thesis, testing of reconstructed signals using the algorithms takes place and results are evaluated by objective measures SDR, PEMO-Q, PEAQ and subjective listening test MUSHRA.

abstract: Ultrasound B-mode imaging is an increasingly significant medical imaging modality for clinical applications. Compared to other imaging modalities like computed tomography (CT) or magnetic resonance imaging (MRI), ultrasound imaging has the advantage of being safe, inexpensive, and portable. While two dimensional (2-D) ultrasound imaging is very popular, three dimensional (3-D) ultrasound imaging provides distinct advantages over its 2-D counterpart by providing volumetric imaging, which leads to more accurate analysis of tumor and cysts. However, the amount of received data at the front-end of 3-D system is extremely large, making it impractical for power-constrained portable systems. In this thesis, algorithm and hardware design techniques to support a hand-held 3-D ultrasound imaging system are proposed. Synthetic aperture sequential beamforming (SASB) is chosen since its computations can be split into two stages, where the output generated of Stage 1 is significantly smaller in size compared to the input. This characteristic enables Stage 1 to be done in the front end while Stage 2 can be sent out to be processed elsewhere. The contributions of this thesis are as follows. First, 2-D SASB is extended to 3-D. Techniques to increase the volume rate of 3-D SASB through a new multi-line firing scheme and use of linear chirp as the excitation waveform, are presented. A new sparse array design that not only reduces the number of active transducers but also avoids the imaging degradation caused by grating lobes, is proposed. A combination of these techniques increases the volume rate of 3-D SASB by 4\texttimes{} without introducing extra computations at the front end. Next, algorithmic techniques to further reduce the Stage 1 computations in the front end are presented. These include reducing the number of distinct apodization coefficients and operating with narrow-bit-width fixed-point data. A 3-D die stacked architecture is designed for the front end. This highly parallel architecture enables the signals received by 961 active transducers to be digitalized, routed by a network-on-chip, and processed in parallel. The processed data are accumulated through a bus-based structure. This architecture is synthesized using TSMC 28 nm technology node and the estimated power consumption of the front end is less than 2 W. Finally, the Stage 2 computations are mapped onto a reconfigurable multi-core architecture, TRANSFORMER, which supports different types of on-chip memory banks and run-time reconfigurable connections between general processing elements and memory banks. The matched filtering step and the beamforming step in Stage 2 are mapped onto TRANSFORMER with different memory configurations. Gem5 simulations show that the private cache mode generates shorter execution time and higher computation efficiency compared to other cache modes. The overall execution time for Stage 2 is 14.73 ms. The average power consumption and the average Giga-operations-per-second/Watt in 14 nm technology node are 0.14 W and 103.84, respectively. / Dissertation/Thesis / Doctoral Dissertation Engineering 2019

Deep nueral networks (DNNs) have become popular due to their predictive power and flexibility in model fitting. In unsupervised learning, variational autoencoders (VAEs) and generative adverarial networks (GANs) are two most popular and successful generative models. How to provide a unifying framework combining the best of VAEs and GANs in a principled way is a challenging task. In supervised learning, the demand for high-dimensional data analysis has grown significantly, especially in the applications of social networking, bioinformatics, and neuroscience. How to simultaneously approximate the true underlying nonlinear system and identify relevant features based on high-dimensional data (typically with the sample size smaller than the dimension, a.k.a. small-n-large-p) is another challenging task.<div><br></div><div>In this dissertation, we have provided satisfactory answers for these two challenges. In addition, we have illustrated some promising applications using modern machine learning methods.<br></div><div><br></div><div>In the first chapter, we introduce a novel inferential Wasserstein GAN (iWGAN) model, which is a principled framework to fuse auto-encoders and WGANs. GANs have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player training of GANs but has other defects such as mode collapse and lack of metric to detect the convergence. The iWGAN model jointly learns an encoder network and a generator network motivated by the iterative primal dual optimization process. The encoder network maps the observed samples to the latent space and the generator network maps the samples from the latent space to the data space. We establish the generalization error bound of iWGANs to theoretically justify the performance of iWGANs. We further provide a rigorous probabilistic interpretation of our model under the framework of maximum likelihood estimation. The iWGAN, with a clear stopping criteria, has many advantages over other autoencoder GANs. The empirical experiments show that the iWGAN greatly mitigates the symptom of mode collapse, speeds up the convergence, and is able to provide a measurement of quality check for each individual sample. We illustrate the ability of iWGANs by obtaining a competitive and stable performance with state-of-the-art for benchmark datasets. <br></div><div><br></div><div>In the second chapter, we present a general framework for high-dimensional nonlinear variable selection using deep neural networks under the framework of supervised learning. The network architecture includes both a selection layer and approximation layers. The problem can be cast as a sparsity-constrained optimization with a sparse parameter in the selection layer and other parameters in the approximation layers. This problem is challenging due to the sparse constraint and the nonconvex optimization. We propose a novel algorithm, called Deep Feature Selection, to estimate both the sparse parameter and the other parameters. Theoretically, we establish the algorithm convergence and the selection consistency when the objective function has a Generalized Stable Restricted Hessian. This result provides theoretical justifications of our method and generalizes known results for high-dimensional linear variable selection. Simulations and real data analysis are conducted to demonstrate the superior performance of our method.<br></div><div><br></div><div><div>In the third chapter, we develop a novel methodology to classify the electrocardiograms (ECGs) to normal, atrial fibrillation and other cardiac dysrhythmias as defined by the Physionet Challenge 2017. More specifically, we use piecewise linear splines for the feature selection and a gradient boosting algorithm for the classifier. In the algorithm, the ECG waveform is fitted by a piecewise linear spline, and morphological features related to the piecewise linear spline coefficients are extracted. XGBoost is used to classify the morphological coefficients and heart rate variability features. The performance of the algorithm was evaluated by the PhysioNet Challenge database (3658 ECGs classified by experts). Our algorithm achieves an average F1 score of 81% for a 10-fold cross validation and also achieved 81% for F1 score on the independent testing set. This score is similar to the top 9th score (81%) in the official phase of the Physionet Challenge 2017.</div></div><div><br></div><div>In the fourth chapter, we introduce a novel region-selection penalty in the framework of image-on-scalar regression to impose sparsity of pixel values and extract active regions simultaneously. This method helps identify regions of interest (ROI) associated with certain disease, which has a great impact on public health. Our penalty combines the Smoothly Clipped Absolute Deviation (SCAD) regularization, enforcing sparsity, and the SCAD of total variation (TV) regularization, enforcing spatial contiguity, into one group, which segments contiguous spatial regions against zero-valued background. Efficient algorithm is based on the alternative direction method of multipliers (ADMM) which decomposes the non-convex problem into two iterative optimization problems with explicit solutions. Another virtue of the proposed method is that a divide and conquer learning algorithm is developed, thereby allowing scaling to large images. Several examples are presented and the experimental results are compared with other state-of-the-art approaches. <br></div>

<p>U ovoj disertaciji je predstavljen model koji aproksimira pune kova-<br />rijansne matrice u modelu gausovih mešavina (GMM) sa smanjenim<br />brojem parametara i izračunavanja koji su potrebni za izračunavanje<br />izglednosti. U predloženom modelu inverzne kovarijansne matrice su<br />aproksimirane korišćenjem retke reprezentacije njihovih karakteri-<br />stičnih vektora. Pored samog modela prikazan je i algoritam za<br />estimaciju parametara zasnovan na kriterijumu maksimizacije<br />izgeldnosti. Eksperimentalni rezultati na problemu prepoznavanja<br />govora su pokazali da predloženi model za isti nivo greške kao GMM<br />sa upunim kovarijansnim, redukuje broj parametara za 45%.</p> / <p>This thesis proposes a model which approximates full covariance matrices in<br />Gaussian mixture models with a reduced number of parameters and<br />computations required for likelihood evaluations. In the proposed model<br />inverse covariance (precision) matrices are approximated using sparsely<br />represented eigenvectors. A maximum likelihood algorithm for parameter<br />estimation and its practical implementation are presented. Experimental<br />results on a speech recognition task show that while keeping the word error<br />rate close to the one obtained by GMMs with full covariance matrices, the<br />proposed model can reduce the number of parameters by 45%.</p>

The paper describes a storage scheme for sparse symmetric or nonsymmetric matrices which has been developed and used for many years at the Technical University of Chemnitz. An overview of existing library subroutines using such matrices is included.

Compressed sensing has been a very active area of research and several elegant algorithms have been developed for the recovery of sparse signals in the past few years. However, most of these algorithms are either computationally expensive or make some assumptions that are not suitable for all real world problems. Recently, focus has shifted to Bayesian-based approaches that are able to perform sparse signal recovery at much lower complexity while invoking constraint and/or a priori information about the data. While Bayesian approaches have their advantages, these methods must have access to a priori statistics. Usually, these statistics are unknown and are often difficult or even impossible to predict. An effective workaround is to assume a distribution which is typically considered to be Gaussian, as it makes many signal processing problems mathematically tractable. Seemingly attractive, this assumption necessitates the estimation of the associated parameters; which could be hard if not impossible. In the thesis, we focus on this aspect of Bayesian recovery and present a framework to address the challenges mentioned above. The proposed framework allows Bayesian recovery of sparse signals but at the same time is agnostic to the distribution of the unknown sparse signal components. The algorithms based on this framework are agnostic to signal statistics and utilize a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. In the thesis, we propose several algorithms based on this framework which utilize the structure present in signals for improved recovery. In addition to the algorithm that considers just the sparsity structure of sparse signals, tools that target additional structure of the sparsity recovery problem are proposed. These include several algorithms for a) block-sparse signal estimation, b) joint reconstruction of several common support sparse signals, and c) distributed estimation of sparse signals. Extensive experiments are conducted to demonstrate the power and robustness of our proposed sparse signal estimation algorithms. Specifically, we target the problems of a) channel estimation in massive-MIMO, and b) Narrowband interference mitigation in SC-FDMA. We model these problems as sparse recovery problems and demonstrate how these could be solved naturally using the proposed algorithms.

<p>Real-time global illumination has been a very important topic and is widely used in game industry. Previous offline rendering requires a large amount of time to converge and reduce the noise generated in Monte Carlo method. Thus, it cannot be easily adapted in real-time rendering. Using voxels in the field of global illumination has become a popular approach. While a naïve voxel grid occupies huge memory in video card, a data structure called <i>sparse voxel octree</i> is often implemented in order to reduce memory cost of voxels and achieve efficient ray casting performance in an interactive frame rate. </p> <p>However, rendering of voxels can cause block effects due to the nature of voxel. One solution is to increase the resolution of voxel so that one voxel is smaller than a pixel on screen. But this is usually not feasible because higher resolution results in higher memory consumption. Thus, most of the global illumination methods of SVO (sparse voxel octree) only use it in visibility test and radiance storage, rather than render it directly. Previous research has tried to incorporate SVO in ray tracing, radiosity methods and voxel cone tracing, and all achieved real-time frame rates in complex scenes. However, most of them only focus on static scenes and does not consider dynamic updates of SVO and the influence of it on performance.</p> <p>In this thesis, we will discuss the tradeoff of multiple classic real-time global illumination methods and their implementations using SVO. We will also propose an efficient approach to dynamic update SVO in animated scenes. The deliverables will be implemented in CUDA 11.0 and OpenGL.</p>

In computer games, one use case for artificial intelligence is used to create interesting problems for the player. To do this new techniques such as reinforcement learning allows game developers to create artificial intelligence agents with human-like or superhuman abilities. The Unity ML-agents toolkit is a plugin that provides game developers with access to reinforcement algorithms without expertise in machine learning. In this paper, we compare reinforcement learning methods and provide empirical training data from two different environments. First, we describe the chosen reinforcement methods and then explain the design of both training environments. We compared the benefits in both dense and sparse rewards environments. The reinforcement learning methods were evaluated by comparing the training speed and cumulative rewards of the agents. The goal was to evaluate how much the combination of extrinsic and intrinsic rewards accelerated the training process in the sparse rewards environment. We hope this study helps game developers utilize reinforcement learning more effectively, saving time during the training process by choosing the most fitting training method for their video game environment. The results show that when training reinforcement agents in sparse rewards environments the agents trained faster with the combination of extrinsic and intrinsic rewards. And when training an agent in a sparse reward environment with only extrinsic rewards the agent failed to learn to complete the task.

Clustering is an unsupervised learning technique widely used to group data into homogeneous clusters. For many real-world data containing categorical values, existing algorithms are often computationally costly in high dimensions, do not work well on noisy data with missing values, and rarely provide theoretical guarantees on clustering accuracy. In this thesis, we propose a general categorical data encoding method and a computationally efficient spectral based algorithm to cluster high-dimensional noisy categorical (nominal or ordinal) data. Under a statistical model for data on m attributes from n subjects in r clusters with missing probability epsilon, we show that our algorithm exactly recovers the true clusters with high probability when mn(1-epsilon) >= CMr² log³M, with M=max(n,m) and a fixed constant C. Moreover, we show that mn(1- epsilon)² >= r *delta/2 with 0< delta <1 is necessary for any algorithm to succeed with probability at least (1+delta)/2. In case, where m=n and r is fixed, for example, the sufficient condition matches with the necessary condition up to a polylog(n) factor, showing that our proposed algorithm is nearly optimal. We also show our algorithm outperforms several existing algorithms in both clustering accuracy and computational efficiency, both theoretically and numerically. In addition, we propose a spectral algorithm with standardization to cluster mixed data. This algorithm is computationally efficient and its clustering accuracy has been evaluated numerically on both real world data and synthetic data.