Sparsity Based Formulations For Dereverberation

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2016Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2016Konser, konferans, toplantı gibi ortamlarda kaydedilen akustik işaretler, kaydın alındığı ortam nedeni ile yankıya ve gürültüye maruz kalır. Kaynak işaretinin elde edilen gözlemlerden kestirimi yankı giderme problemi olarak isimlendirilir. Bu kayıtlarda göze çarpan yankı etkileri bir süzgeç olarak zaman tanım bölgesinde modellenebilir. Yankı etkilerini modelleyen bu süzgeç oda darbe cevabı olarak isimlendirilir. Oda darbe cevabının bilindiği durumda problem gözü kapalı olmayan yankı giderme problemine dönüşür. Tez boyunca oda darbe cevabının bilindiği durumlar dikkate alınmıştır. Gözlemlenebilir ki, oda darbe cevabı kaynak ve gözlem noktalarına çok bağımlıdır. Bu nedenle oda darbe cevabının bütün uzaydaki noktalar için kestirimi çok zordur. Bu durumda oda darbe cevapları tezdeki deneylerde sentetik olarak uygulanmış veya gözlem ortamında kayıt alındığı sırada gözlemden elde edilmişlerdir. Bölüm 5, bu duruma farklı bir açıdan bakılmasının örneğidir. Bu bölümde oda darbe cevabının kısmen bilindiği ve gözlem ortamı için tek bir süzgeç tanımlanabileceği durumları göz önüne alınmıştır.Acoustic signals recorded in concerts, meetings or conferences are effected by the room impulse response and noise. Estimating the clean source signals from the observations is referred as the dereverberation problem. If the room impulse responses are known, the problem is non-blind dereverberation problem. In this thesis non-blind dereverberation problem is posed using convex penalty functions, with a convex minimization procedure. The convex minimization problems are solved using iterative methods. Through the thesis sparse nature of the time frequency spectrum is referred. In order to transform the time domain signal to a time frequency spectrum Short Time Fourier Transform is used.Yüksek LisansM.Sc

Hierarchical Bayesian sparse image reconstruction with application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of our hierarchical Bayesian sparse reconstruction method is illustrated on synthetic and real data collected from a tobacco virus sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200

Octonion sparse representation for color and multispectral image processing

A recent trend in color image processing combines the quaternion algebra with dictionary learning methods. This paper aims to present a generalization of the quaternion dictionary learning method by using the octonion algebra. The octonion algebra combined with dictionary learning methods is well suited for representation of multispectral images with up to 7 color channels. Opposed to the classical dictionary learning techniques that treat multispectral images by concatenating spectral bands into a large monochrome image, we treat all the spectral bands simultaneously. Our approach leads to better preservation of color fidelity in true and false color images of the reconstructed multispectral image. To show the potential of the octonion based model, experiments are conducted for image reconstruction and denoising of color images as well as of extensively used Landsat 7 images

Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests