Bayes meets Bach: applications of Bayesian statistics to audio restoration

Memoryless nonlinear distortion can be present in audio signals, from recording to reproduction: bad quality or amateurishly operated equipments, physically degraded media and low quality reproducing devices are some examples where nonlinearities can naturally appear. Another quite common defect in old recordings are the long pulses, caused in general by the reproduction of disks with deep scratches or severely degraded magnetic tapes. Such defects are characterized by an initial discontinuity in the waveform, followed by a low-frequency transient of long duration. In both cases audible artifacts can be created, causing an unpleasant experience to the listener. It is then important to develop techniques to mitigate such defects, having at hand only the degraded signal, in a way to recover the original signal. In this thesis, techniques to deal with both problems are presented: the restoration of nonlinearly degraded recordings is tackled in a Bayesian context, considering both autoregressive models and sparsity in the DCT domain for the original signal, as well as through a deterministic solution also based on sparsity; for the suppression of long pulses, a parametric approach is revisited with the addition of an efficient initialization procedure, and a nonparametric modeling via Gaussian process is also presented.Distorções não-lineares podem aparecer em sinais de áudio desde o momento da sua gravação até a posterior reprodução: equipamentos precários ou operados de maneira indevida, mídias fisicamente degradadas e baixa qualidade dos aparelhos de reprodução são somente alguns exemplos onde não-linearidades podem aparecer de modo natural. Outro defeito bastante comum em gravações antigas são os pulsos longos, em geral causados pela reprodução de discos com arranhões muito profundos ou fitas magnéticas severamente degradadas. Tais defeitos são caracterizados por uma descontinuidade inicial na forma de onda, seguida de um transitório de baixa frequência e longa duração. Em ambos os casos, artefatos auditivos podem ser criados, causando assim uma experiência ruim para o ouvinte. E importante então desenvolver técnicas para mitigar tais efeitos, tendo como base somente uma versão do sinal degradado, de modo a recuperar o sinal original não degradado. Nessa tese são apresentadas técnicas para lidar com esses dois problemas: o problema de restaurar gravações corrompidas com distorções não-lineares é abordado em um contexto bayesiano, considerando tanto modelos autorregressivos quanto de esparsidade no domínio da DCT para o sinal original, bem como por uma solução determinística também em usando esparsidade; para a supressão de pulsos longos, uma abordagem paramétrica é revisitada, junto com o acréscimo de um eficiente procedimento de inicialização, sendo também apresentada uma abordagem não-paramétricausando processos gaussianos

Custom optimization algorithms for efficient hardware implementation

The focus is on real-time optimal decision making with application in advanced control systems. These computationally intensive schemes, which involve the repeated solution of (convex) optimization problems within a sampling interval, require more efficient computational methods than currently available for extending their application to highly dynamical systems and setups with resource-constrained embedded computing platforms. A range of techniques are proposed to exploit synergies between digital hardware, numerical analysis and algorithm design. These techniques build on top of parameterisable hardware code generation tools that generate VHDL code describing custom computing architectures for interior-point methods and a range of first-order constrained optimization methods. Since memory limitations are often important in embedded implementations we develop a custom storage scheme for KKT matrices arising in interior-point methods for control, which reduces memory requirements significantly and prevents I/O bandwidth limitations from affecting the performance in our implementations. To take advantage of the trend towards parallel computing architectures and to exploit the special characteristics of our custom architectures we propose several high-level parallel optimal control schemes that can reduce computation time. A novel optimization formulation was devised for reducing the computational effort in solving certain problems independent of the computing platform used. In order to be able to solve optimization problems in fixed-point arithmetic, which is significantly more resource-efficient than floating-point, tailored linear algebra algorithms were developed for solving the linear systems that form the computational bottleneck in many optimization methods. These methods come with guarantees for reliable operation. We also provide finite-precision error analysis for fixed-point implementations of first-order methods that can be used to minimize the use of resources while meeting accuracy specifications. The suggested techniques are demonstrated on several practical examples, including a hardware-in-the-loop setup for optimization-based control of a large airliner.Open Acces