Approved for public release, distribution is unlimited / "This work accomplishes signal denoising using the Bootstrap method when the additive noise is Gaussian. The noisy signal is separated into frequency bands using the Fourier or Wavelet transform. Each frequency band is tested for Gaussianity by evaluating the kurtosis. The Bootstrap method is used to increase the reliability of the kurtosis estimate. Noise effects are minimized using a hard or soft thresholding scheme on the frequency bands that were estimated to be Gaussian. The recovered signal is obtained by applying the appropriate inverse transform to the modified frequency bands. The denoising scheme is tested using three test signals. Results show that FFT-based denoising schemes perform better than WT-based denoising schemes on the stationary sinusoidal signals, whereas WT-based schemes outperform FFT-based schemes on chirp type signals. Results also show that hard thresholding never outperforms soft thresholding, at best its performance is similar to soft thresholding."--p.i. / First Lieutenant, Turkish Army

A novel technique for blind deconvolution of ultrasound is introduced. Existing deconvolution techniques for ultrasound such as cepstrum-based methods and the work of Adam and Michailovich – based on Discrete Wavelet Transform (DWT) shrinkage of the log-spectrum – exploit the smoothness of the pulse log-spectrum relative to the reflectivity function to estimate the pulse. To reduce the effects of non-stationarity in the ultrasound signal on both the pulse estimation and deconvolution, the log-spectrum is time-localized and represented as the Continuous Wavelet Transform (CWT) log-scalogram in the proposed technique. The pulse CWT coefficients are estimated via DWT shrinkage of the log-scalogram and are then deconvolved by wavelet-domain Wiener filtering. Parameters of the technique are found by heuristic optimization on a training set with various quality metrics: entropy, autocorrelation 6-dB width and fractal dimension. The technique is further enhanced by using different CWT wavelets for estimation and deconvolution, similar to the WienerChop method.

A novel technique for blind deconvolution of ultrasound is introduced. Existing deconvolution techniques for ultrasound such as cepstrum-based methods and the work of Adam and Michailovich – based on Discrete Wavelet Transform (DWT) shrinkage of the log-spectrum – exploit the smoothness of the pulse log-spectrum relative to the reflectivity function to estimate the pulse. To reduce the effects of non-stationarity in the ultrasound signal on both the pulse estimation and deconvolution, the log-spectrum is time-localized and represented as the Continuous Wavelet Transform (CWT) log-scalogram in the proposed technique. The pulse CWT coefficients are estimated via DWT shrinkage of the log-scalogram and are then deconvolved by wavelet-domain Wiener filtering. Parameters of the technique are found by heuristic optimization on a training set with various quality metrics: entropy, autocorrelation 6-dB width and fractal dimension. The technique is further enhanced by using different CWT wavelets for estimation and deconvolution, similar to the WienerChop method.

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With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of discrepancies between clean and denoised images occur at feature edges, this study examines several convolution-based edge detection methods to isolate relevant feature. The resultant gradient and edge information is used to further parameterize the ��−means non-local method. An additional hybrid method involving the combined contributions of variational and ��−means non-local denoising is proposed, with the weighting determined by edge intensities. This method outperforms the other methods outlined in the study, both conventional and newly presented.

This dissertation addresses the problem of adaptive image filtering. Although the topic has a long history in the image processing community, researchers continuously present novel methods to obtain ever better image restoration results. With an expanding market for individuals who wish to share their everyday life on social media, imaging techniques such as compact cameras and smart phones are important factors. Naturally, every producer of imaging equipment desires to exploit cheap camera components while supplying high quality images. One step in this pipeline is to use sophisticated imaging software including, e.g., noise reduction to reduce manufacturing costs, while maintaining image quality. This thesis is based on traditional formulations such as isotropic and tensor-based anisotropic diffusion for image denoising. The difference from main-stream denoising methods is that this thesis explores the effects of introducing contextual information as prior knowledge for image denoising into the filtering schemes. To achieve this, the adaptive filtering theory is formulated from an energy minimization standpoint. The core contributions of this work is the introduction of a novel tensor-based functional which unifies and generalises standard diffusion methods. Additionally, the explicit Euler-Lagrange equation is derived which, if solved, yield the stationary point for the minimization problem. Several aspects of the functional are presented in detail which include, but are not limited to, tensor symmetry constraints and convexity. Also, the classical problem of finding a variational formulation to a given tensor-based partial differential equation is studied. The presented framework is applied in problem formulation that includes non-linear domain transformation, e.g., visualization of medical images. Additionally, the framework is also used to exploit locally estimated probability density functions or the channel representation to drive the filtering process. Furthermore, one of the first truly tensor-based formulations of total variation is presented. The key to the formulation is the gradient energy tensor, which does not require spatial regularization of its tensor components. It is shown empirically in several computer vision applications, such as corner detection and optical flow, that the gradient energy tensor is a viable replacement for the commonly used structure tensor. Moreover, the gradient energy tensor is used in the traditional tensor-based anisotropic diffusion scheme. This approach results in significant improvements in computational speed when the scheme is implemented on a graphical processing unit compared to using the commonly used structure tensor. / VIDI / NACIP / GARNICS / EMC^2

This thesis is concerned with the solutions to several issues, including the problems of joint localisation, motion de-noising/smoothing, and soft tissue artefacts correction, in skeletal motion reconstruction for motion analysis, using marker-based optical motion capture technologies. We propose a very efficient joint localisation method, which only needs to optimise over three parameters, regardless of the total numbers of markers and frames. A framework powered by this joint localisation solution is also developed, which can automatically find all the joints in an articulated body structure, and significantly reduce the total number of markers needed in a typical motion capture session, by implementing a solvability propagation process. This framework is also configured to operate in a hybrid scheme, which can automatically switch between the primary joint estimator and a slower solution having fewer conditions regarding the required number of markers on a given body segment. This makes the framework workable even for extreme scenarios in which there are fewer than three markers on any body segment. A non-linear optimisation method for 3D trajectory smoothing is also proposed for de-noising the estimated joint paths. By immobilising a series of characteristic points in the trajectory, this method is able to effectively preserve detailed information for vigorous motion sequences. Various other smoothing techniques in the literature are also discussed and compared, concluding that a size-3 weighted average filter implemented in an automatic manner is a good real-time solution for low intensity activities. The effects of skin deformation on marker position data, known as soft tissue artefacts, are learned via a behavioural study on the human upper-body, with specific emphasis on combined limb actions. Based on the experimental findings, mathematical models are proposed to characterise the development of different types of artefacts, including translational, rotational, and transverse. We also theoretically demonstrate the feasibility of using a Kalman filter to correct the soft tissue artefacts, using the mathematical models.

Protein identification has been more helpful than before in the diagnosis and treatment of many diseases, such as cancer, heart disease and HIV. Tandem mass spectrometry is a powerful tool for protein identification. In a typical experiment, proteins are broken into small amino acid oligomers called peptides. By determining the amino acid sequence of several peptides of a protein, its whole amino acid sequence can be inferred. Therefore, peptide identification is the first step and a central issue for protein identification. Tandem mass spectrometers can produce a large number of tandem mass spectra which are used for peptide identification. Two issues should be addressed to improve the performance of current peptide identification algorithms. Firstly, nearly all spectra are noise-contaminated. As a result, the accuracy of peptide identification algorithms may suffer from the noise in spectra. Secondly, the majority of spectra are not identifiable because they are of too poor quality. Therefore, much time is wasted attempting to identify these unidentifiable spectra.<p> The goal of this research is to design spectrum pre-processing algorithms to both speedup and improve the reliability of peptide identification from tandem mass spectra. Firstly, as a tandem mass spectrum is a one dimensional signal consisting of dozens to hundreds of peaks, and majority of peaks are noisy peaks, a spectrum denoising algorithm is proposed to remove most noisy peaks of spectra. Experimental results show that our denoising algorithm can remove about 69% of peaks which are potential noisy peaks among a spectrum. At the same time, the number of spectra that can be identified by Mascot algorithm increases by 31% and 14% for two tandem mass spectrum datasets. Next, a two-stage recursive feature elimination based on support vector machines (SVM-RFE) and a sparse logistic regression method are proposed to select the most relevant features to describe the quality of tandem mass spectra. Our methods can effectively select the most relevant features in terms of performance of classifiers trained with the different number of features. Thirdly, both supervised and unsupervised machine learning methods are used for the quality assessment of tandem mass spectra. A supervised classifier, (a support vector machine) can be trained to remove more than 90% of poor quality spectra without removing more than 10% of high quality spectra. Clustering methods such as model-based clustering are also used for quality assessment to cancel the need for a labeled training dataset and show promising results.

Protein identification has been more helpful than before in the diagnosis and treatment of many diseases, such as cancer, heart disease and HIV. Tandem mass spectrometry is a powerful tool for protein identification. In a typical experiment, proteins are broken into small amino acid oligomers called peptides. By determining the amino acid sequence of several peptides of a protein, its whole amino acid sequence can be inferred. Therefore, peptide identification is the first step and a central issue for protein identification. Tandem mass spectrometers can produce a large number of tandem mass spectra which are used for peptide identification. Two issues should be addressed to improve the performance of current peptide identification algorithms. Firstly, nearly all spectra are noise-contaminated. As a result, the accuracy of peptide identification algorithms may suffer from the noise in spectra. Secondly, the majority of spectra are not identifiable because they are of too poor quality. Therefore, much time is wasted attempting to identify these unidentifiable spectra.<p> The goal of this research is to design spectrum pre-processing algorithms to both speedup and improve the reliability of peptide identification from tandem mass spectra. Firstly, as a tandem mass spectrum is a one dimensional signal consisting of dozens to hundreds of peaks, and majority of peaks are noisy peaks, a spectrum denoising algorithm is proposed to remove most noisy peaks of spectra. Experimental results show that our denoising algorithm can remove about 69% of peaks which are potential noisy peaks among a spectrum. At the same time, the number of spectra that can be identified by Mascot algorithm increases by 31% and 14% for two tandem mass spectrum datasets. Next, a two-stage recursive feature elimination based on support vector machines (SVM-RFE) and a sparse logistic regression method are proposed to select the most relevant features to describe the quality of tandem mass spectra. Our methods can effectively select the most relevant features in terms of performance of classifiers trained with the different number of features. Thirdly, both supervised and unsupervised machine learning methods are used for the quality assessment of tandem mass spectra. A supervised classifier, (a support vector machine) can be trained to remove more than 90% of poor quality spectra without removing more than 10% of high quality spectra. Clustering methods such as model-based clustering are also used for quality assessment to cancel the need for a labeled training dataset and show promising results.

In this paper, we turn the interpolation problem of coarsely-sampled data into a denoising problem. From this point of view, we illustrate the benefit of random sampling at sub-Nyquist rate over regular sampling at the same rate. We show that, using nonlinear sparsity promoting optimization, coarse random sampling may actually lead to significantly better wavefield reconstruction than equivalent regularly sampled data.