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.

<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>

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In this dissertation, the general problem of the dimensionality reduction of hyperspectral imagery is considered. Data dimension can be reduced through compression, in which an original image is encoded into bitstream of greatly reduced size; through application of a transformation, in which a high-dimensional space is mapped into a low-dimensional space; and through a simple process of subsampling, wherein the number of pixels is reduced spatially during image acquisition. All three techniques are investigated in the course of the dissertation. For data compression, an approach to calculate an operational bitrate for JPEG2000 in conjunction with principal component analysis is proposed. It is shown that an optimal bitrate for such a lossy compression method can be estimated while maintaining both class separability as well as anomalous pixels in the original data. On the other hand, the transformation paradigm is studied for spectral dimensionality reduction; specifically, dataindependent random spectral projections are considered, while the compressive projection principal component analysis algorithm is adopted for data reconstruction. It is shown that, by incorporating both spectral and spatial partitioning of the original data, reconstruction accuracy can be improved. Additionally, a new supervised spectral dimensionality reduction approach using a sparsity-preserving graph is developed. The resulting sparse graph-based discriminant analysis is seen to yield superior classification performance at low dimensionality. Finally, for spatial dimensionality reduction, a simple spatial subsampling scheme is considered for a multitemporal hyperspectral image sequence, such that the original image is reconstructed using a sparse dictionary learned from a prior image in the sequence.

Typically, inverse imaging problems deal with the reconstruction of images from the sensor measurements where sensors can take form of any imaging modality like camera, radar, hyperspectral or medical imaging systems. In an ideal scenario, we can reconstruct the images via applying an inversion procedure from these sensors’ measurements, but practical applications have several challenges: the measurement acquisition process is heavily corrupted by the noise, the forward model is not exactly known, and non-linearities or unknown physics of the data acquisition play roles. Hence, perfect inverse function is not exactly known for immaculate image reconstruction. To this end, in this dissertation, I propose an automatic sensing and reconstruction scheme based on deep learning within the compressive sensing (CS) framework to solve the computational imaging problems. Here, I develop a data-driven approach to learn both the measurement matrix and the inverse reconstruction scheme for a given class of signals, such as images. This approach paves the way for end-to-end learning and reconstruction of signals with the aid of cascaded fully connected and multistage convolutional layers with a weighted loss function in an adversarial learning framework. I also propose to extend our analysis to introduce data driven models to directly classify from compressed measurements through joint reconstruction and classification. I develop constrained measurement learning framework and demonstrate higher performance of the proposed approach in the field of typical image reconstruction and hyperspectral image classification tasks. Finally, I also propose a single data driven network that can take and reconstruct images at multiple rates of signal acquisition. In summary, this dissertation proposes novel methods on the data driven measurement acquisition for sparse signal reconstruction and classification, learning measurements for given constraints underlying the requirement of the hardware for different applications, and producing a common data driven platform for learning measurements to reconstruct signals at multiple rates. This dissertation opens the path to the learned sensing systems. The future research can use these proposed data driven approaches as the pivotal factors to accomplish task-specific smart sensors in several real-world applications.

With the increasing pervasiveness of digital cameras, the Internet, and social networking, there is a growing need to catalog and analyze large collections of photos and videos. In this dissertation, we explore unconstrained still-image and video-based face recognition in real-world scenarios, e.g. social photo sharing and movie trailers, where people of interest are recognized and all others are ignored. In such a scenario, we must obtain high precision in recognizing the known identities, while accurately rejecting those of no interest. Recent advancements in face recognition research has seen Sparse Representation-based Classification (SRC) advance to the forefront of competing methods. However, its drawbacks, slow speed and sensitivity to variations in pose, illumination, and occlusion, have hindered its wide-spread applicability. The contributions of this dissertation are three-fold: 1. For still-image data, we propose a novel Linearly Approximated Sparse Representation-based Classification (LASRC) algorithm that uses linear regression to perform sample selection for l1-minimization, thus harnessing the speed of least-squares and the robustness of SRC. On our large dataset collected from Facebook, LASRC performs equally to standard SRC with a speedup of 100-250x. 2. For video, applying the popular l1-minimization for face recognition on a frame-by-frame basis is prohibitively expensive computationally, so we propose a new algorithm Mean Sequence SRC (MSSRC) that performs video face recognition using a joint optimization leveraging all of the available video data and employing the knowledge that the face track frames belong to the same individual. Employing MSSRC results in a speedup of 5x on average over SRC on a frame-by-frame basis. 3. Finally, we make the observation that MSSRC sometimes assigns inconsistent identities to the same individual in a scene that could be corrected based on their visual similarity. Therefore, we construct a probabilistic affinity graph combining appearance and co-occurrence similarities to model the relationship between face tracks in a video. Using this relationship graph, we employ random walk analysis to propagate strong class predictions among similar face tracks, while dampening weak predictions. Our method results in a performance gain of 15.8% in average precision over using MSSRC alone.

High frame rate video (HFV) is an important investigational tool in sciences, engineering and military. In ultrahigh speed imaging, the obtainable temporal, spatial and spectral resolutions are limited by the sustainable throughput of in-camera mass memory, the lower bound of exposure time, and illumination conditions. In order to break these bottlenecks, we propose a new coded video acquisition framework that employs K>1 cameras, each of which makes random measurements of the video signal in both temporal and spatial domains. For each of the K cameras, this multi-camera strategy greatly relaxes the stringent requirements in memory speed, shutter speed, and illumination strength. The recovery of HFV from these random measurements is posed and solved as a large scale l1 minimization problem by exploiting joint temporal and spatial sparsities of the 3D signal. Three coded video acquisition techniques of varied trade o s between performance and hardware complexity are developed: frame-wise coded acquisition, pixel-wise coded acquisition, and column-row-wise coded acquisition. The performances of these techniques are analyzed in relation to the sparsity of the underlying video signal. To make ultra high speed cameras of coded exposure more practical and a fordable, we develop a coded exposure video/image acquisition system by an innovative assembling of multiple rolling shutter cameras. Each of the constituent rolling shutter cameras adopts a random pixel read-out mechanism by simply changing the read out order of pixel rows from sequential to random. Simulations of these new image/video coded acquisition techniques are carried out and experimental results are reported. / Dissertation / Doctor of Philosophy (PhD)

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In signal processing field, there are various measures that can be employed to analyse and represent the signal in order to obtain meaningful outcome. Sparse representation (SR) has continued to receive great attention as one of the well-known tools in statistical theory which among others, is used to extract specific latent temporal features that can reveal salient primitive and sparsely represented features of complex data signals, including temporal data analysis. Under reasonable conditions, many signals are assumed to be sparse within a domain, such as spatial, time, or timefrequency domain, and this sparse characteristics of such signals can be obtained through the SR. The ECG signal, for instance, is typically a temporal sparse signal, comprises of various periodic activities such as time delay and frequency amplitudes, plus additive noise and possible interference. Particularly challenging in signal processing, especially time series signals is how to reconstruct and extract the various features that characterized the signal. Many problems (e.g., signal components analysis, feature extraction/selection in signals, signal reconstruction, and classification) can be formulated as linear models and solved using the SR technique The reconstruction of signals through SR can offer a rich representation of the sparsified temporal structure of the original signal. Due to its numerous advantages, such as noise tolerance and widespread use in various signal processing tasks, this has motivated many researchers to adopt the use of this technique for various signal representation analysis for a better and richer representation of the original input signal. In line with this, therefore, the goal of this study is to propose a SR-based mathematical framework and a coherence function for reconstruction and feature extraction from signals for subsequent analysis. The time embedding principle was first applied to restructure the signal into tine delay vectors and then the proposed approach, referred to as temporal subsequence SR approach was used to reconstruct the noisy signals and provides a sparsified time dependent input signal representation, and then the coherence function is further used to compute and extract the correlational coefficient quantities between the temporal subsequence signals to form the final feature vectors representing the discriminative features for each of the signal. These final feature vectors representing the signal are further used as inputs to machine learning classifiers. Experiments are carried out to illustrate the usefulness of the proposed methods and to assess their impact on the classification performance of the SVM and MLP classifiers using the popular and widely used ECG time series benchmark dataset. This research study supports the general hypothesis that, signal reconstruction methods (datadriven approach) can be valuable in learning compact features from the original signals for classifications.

Num cenário em que dispositivos de aquisição de imagens e vídeo possuem recursos limitados ou as imagens disponíveis não possuem boa qualidade, as técnicas de super-resolução (SR) apresentam uma excelente alternativa para melhorar a qualidade das imagens. Nesta tese é apresentada uma proposta para super-resolução de imagem única que combina os benefícios da interpolação no domínio da transformada DCT e a eficiência dos métodos de reconstrução baseados no conceito de representação esparsa de sinais. A proposta busca aproveitar as melhorias já alcançadas na qualidade e eficiência computacional dos principais algoritmos de super-resolução existentes. O método de super-resolução proposto implementa algumas melhorias nas etapas de treinamento e reconstrução da imagem final. Na etapa de treinamento foi incluída uma nova etapa de extração de características utilizando técnicas de aguçamento por máscara de nitidez e construção de um novo dicionário. Esta estratégia busca extrair mais informações estruturais dos fragmentos de baixa e alta resolução do conjunto de treinamento e ao mesmo tempo reduzir o tamanho dos dicionários. Outra importante contribuição foi a inclusão de um processo iterativo e escalonável no algoritmo, reinserindo no conjunto de treinamento e na etapa de reconstrução, uma imagem de alta resolução obtida numa primeira iteração. Esta solução possibilitou uma melhora na qualidade da imagem de alta resolução final utilizando poucas imagens no conjunto de treinamento. As simulações computacionais demonstraram a capacidade do método proposto em produzir imagens com qualidade e com tempo computacional reduzido. / In a scenario in which the acquisition systems have limited resources or available images do not have good quality, the super-resolution (SR) techniques have become an excellent alternative for improving the image quality. In this thesis, we propose a single-image super-resolution (SR) method that combines the benefits of the DCT interpolation and efficiency of sparse representation method for image reconstruction. Also, the proposed method seeks to take advantage of the improvements already achieved in quality and computational efficiency of the existing SR algorithms. The proposed method implements some improvements in the dictionary training and the reconstruction process. A new dictionary was built by using an unsharp mask technique to characteristics extraction. Simultaneously, this strategy aim to extract more structural information of the low resolution and high resolution patches and reduce the dictionaries size. Another important contribution was the inclusion of an iterative and scalable process by reinserting the HR image obtained of first iteration. This solution aim to improve the quality of the final HR image using a few images in the training set. The results have demonstrated the ability of the proposed method to produce high quality images with reduced computational time.