Extreme Value Analysis of Empirical Frame Coefficients and Implications for Denoising by Soft-Thresholding

Denoising by frame thresholding is one of the most basic and efficient methods for recovering a discrete signal or image from data that are corrupted by additive Gaussian white noise. The basic idea is to select a frame of analyzing elements that separates the data in few large coefficients due to the signal and many small coefficients mainly due to the noise \epsilon_n. Removing all data coefficients being in magnitude below a certain threshold yields a reconstruction of the original signal. In order to properly balance the amount of noise to be removed and the relevant signal features to be kept, a precise understanding of the statistical properties of thresholding is important. For that purpose we derive the asymptotic distribution of max_{\omega \in \Omega_n} || for a wide class of redundant frames (\phi_\omega^n: \omega \in \Omega_n}. Based on our theoretical results we give a rationale for universal extreme value thresholding techniques yielding asymptotically sharp confidence regions and smoothness estimates corresponding to prescribed significance levels. The results cover many frames used in imaging and signal recovery applications, such as redundant wavelet systems, curvelet frames, or unions of bases. We show that `generically' a standard Gumbel law results as it is known from the case of orthonormal wavelet bases. However, for specific highly redundant frames other limiting laws may occur. We indeed verify that the translation invariant wavelet transform shows a different asymptotic behaviour.Comment: [Content: 39 pages, 4 figures] Note that in this version 4 we have slightely changed the title of the paper and we have rewritten parts of the introduction. Except for corrected typos the other parts of the paper are the same as the original versions

An Adaptive Weighted Average (WAV) Reprojection Algorithm for Image Denoising

Patch-based denoising algorithms have an effective improvement in the image denoising domain. The Non-Local Means (NLM) algorithm is the most popular patch-based spatial domain denoising algorithm. Many variants of the NLM algorithm have proposed to improve its performance. Weighted Average (WAV) reprojection algorithm is one of the most effective improvements of the NLM denoising algorithm. Contrary to the NLM algorithm, all the pixels in the patch contribute into the averaging process in the WAV reprojection algorithm, which enhances the denoising performance. The key parameters in the WAV reprojection algorithm are kept fixed regardless of the image structure. In this thesis, an improved WAV reprojection algorithm is proposed, where the patch size is assigned adaptively based on the image structure. The image structure is identified using an improved classification method that is based on the structure tensor matrix. The classification result is also utilized to improve the identification of similar patches in the image. The experimental results show that the denoising performance of the proposed method is better than that of the original WAV reprojection algorithm, as well as some other variants of the NLM algorithm

Unifying the Visible and Passive Infrared Bands: Homogeneous and Heterogeneous Multi-Spectral Face Recognition

Face biometrics leverages tools and technology in order to automate the identification of individuals. In most cases, biometric face recognition (FR) can be used for forensic purposes, but there remains the issue related to the integration of technology into the legal system of the court. The biggest challenge with the acceptance of the face as a modality used in court is the reliability of such systems under varying pose, illumination and expression, which has been an active and widely explored area of research over the last few decades (e.g. same-spectrum or homogeneous matching). The heterogeneous FR problem, which deals with matching face images from different sensors, should be examined for the benefit of military and law enforcement applications as well. In this work we are concerned primarily with visible band images (380-750 nm) and the infrared (IR) spectrum, which has become an area of growing interest.;For homogeneous FR systems, we formulate and develop an efficient, semi-automated, direct matching-based FR framework, that is designed to operate efficiently when face data is captured using either visible or passive IR sensors. Thus, it can be applied in both daytime and nighttime environments. First, input face images are geometrically normalized using our pre-processing pipeline prior to feature-extraction. Then, face-based features including wrinkles, veins, as well as edges of facial characteristics, are detected and extracted for each operational band (visible, MWIR, and LWIR). Finally, global and local face-based matching is applied, before fusion is performed at the score level. Although this proposed matcher performs well when same-spectrum FR is performed, regardless of spectrum, a challenge exists when cross-spectral FR matching is performed. The second framework is for the heterogeneous FR problem, and deals with the issue of bridging the gap across the visible and passive infrared (MWIR and LWIR) spectrums. Specifically, we investigate the benefits and limitations of using synthesized visible face images from thermal and vice versa, in cross-spectral face recognition systems when utilizing canonical correlation analysis (CCA) and locally linear embedding (LLE), a manifold learning technique for dimensionality reduction. Finally, by conducting an extensive experimental study we establish that the combination of the proposed synthesis and demographic filtering scheme increases system performance in terms of rank-1 identification rate

Wavelet-based noise reduction of cDNA microarray images

The advent of microarray imaging technology has lead to enormous progress in the life sciences by allowing scientists to analyze the expression of thousands of genes at a time. For complementary DNA (cDNA) microarray experiments, the raw data are a pair of red and green channel images corresponding to the treatment and control samples. These images are contaminated by a high level of noise due to the numerous noise sources affecting the image formation. A major challenge of microarray image analysis is the extraction of accurate gene expression measurements from the noisy microarray images. A crucial step in this process is denoising, which consists of reducing the noise in the observed microarray images while preserving the signal information as much as possible. This thesis deals with the problem of developing novel methods for reducing noise in cDNA microarray images for accurate estimation of the gene expression levels. Denoising methods based on the wavelet transform have shown significant success when applied to natural images. However, these methods are not very efficient for reducing noise in cDNA microarray images. An important reason for this is that existing methods are only capable of processing the red and green channel images separately. In doing so. they ignore the signal correlation as well as the noise correlation that exists between the wavelet coefficients of the two channels. The primary objective of this research is to design efficient wavelet-based noise reduction algorithms for cDNA microarray images that take into account these inter-channel dependencies by 'jointly' estimating the noise-free coefficients in both the channels. Denoising algorithms are developed using two types of wavelet transforms, namely, the frequently-used discrete wavelet transform (DWT) and the complex wavelet transform (CWT). The main advantage of using the DWT for denoising is that this transform is computationally very efficient. In order to obtain a better denoising performance for microarray images, however, the CWT is preferred to DWT because the former has good directional selectivity properties that are necessary for better representation of the circular edges of spots. The linear minimum mean squared error and maximum a posteriori estimation techniques are used to develop bivariate estimators for the noise-free coefficients of the two images. These estimators are derived by utilizing appropriate joint probability density functions for the image coefficients as well as the noise coefficients of the two channels. Extensive experimentations are carried out on a large set of cDNA microarray images to evaluate the performance of the proposed denoising methods as compared to the existing ones. Comparisons are made using standard metrics such as the peak signal-to-noise ratio (PSNR) for measuring the amount of noise removed from the pixels of the images, and the mean absolute error for measuring the accuracy of the estimated log-intensity ratios obtained from the denoised version of the images. Results indicate that the proposed denoising methods that are developed specifically for the microarray images do, indeed, lead to more accurate estimation of gene expression levels. Thus, it is expected that the proposed methods will play a significant role in improving the reliability of the results obtained from practical microarray experiments

Towards to optimal wavelet denoising scheme - A novel spatial and volumetric mapping of wavelet-based biomedical data smoothing

Wavelet transformation is one of the most frequent procedures for data denoising, smoothing, decomposition, features extraction, and further related tasks. In order to perform such tasks, we need to select appropriate wavelet settings, including particular wavelet, decomposition level and other parameters, which form the wavelet transformation outputs. Selection of such parameters is a challenging area due to absence of versatile recommendation tools for suitable wavelet settings. In this paper, we propose a versatile recommendation system for prediction of suitable wavelet selection for data smoothing. The proposed system is aimed to generate spatial response matrix for selected wavelets and the decomposition levels. Such response enables the mapping of selected evaluation parameters, determining the efficacy of wavelet settings. The proposed system also enables tracking the dynamical noise influence in the context of Wavelet efficacy by using volumetric response. We provide testing on computed tomography (CT) and magnetic resonance (MR) image data and EMG signals mostly of musculoskeletal system to objectivise system usability for clinical data processing. The experimental testing is done by using evaluation parameters such is MSE (Mean Squared Error), ED (Euclidean distance) and Corr (Correlation index). We also provide the statistical analysis of the results based on Mann-Whitney test, which points out on statistically significant differences for individual Wavelets for the data corrupted with Salt and Pepper and Gaussian noise.Web of Science2018art. no. 530

Textural Difference Enhancement based on Image Component Analysis

In this thesis, we propose a novel image enhancement method to magnify the textural differences in the images with respect to human visual characteristics. The method is intended to be a preprocessing step to improve the performance of the texture-based image segmentation algorithms. We propose to calculate the six Tamura's texture features (coarseness, contrast, directionality, line-likeness, regularity and roughness) in novel measurements. Each feature follows its original understanding of the certain texture characteristic, but is measured by some local low-level features, e.g., direction of the local edges, dynamic range of the local pixel intensities, kurtosis and skewness of the local image histogram. A discriminant texture feature selection method based on principal component analysis (PCA) is then proposed to find the most representative characteristics in describing textual differences in the image. We decompose the image into pairwise components representing the texture characteristics strongly and weakly, respectively. A set of wavelet-based soft thresholding methods are proposed as the dictionaries of morphological component analysis (MCA) to sparsely highlight the characteristics strongly and weakly from the image. The wavelet-based thresholding methods are proposed in pair, therefore each of the resulted pairwise components can exhibit one certain characteristic either strongly or weakly. We propose various wavelet-based manipulation methods to enhance the components separately. For each component representing a certain texture characteristic, a non-linear function is proposed to manipulate the wavelet coefficients of the component so that the component is enhanced with the corresponding characteristic accentuated independently while having little effect on other characteristics. Furthermore, the above three methods are combined into a uniform framework of image enhancement. Firstly, the texture characteristics differentiating different textures in the image are found. Secondly, the image is decomposed into components exhibiting these texture characteristics respectively. Thirdly, each component is manipulated to accentuate the corresponding texture characteristics exhibited there. After re-combining these manipulated components, the image is enhanced with the textural differences magnified with respect to the selected texture characteristics. The proposed textural differences enhancement method is used prior to both grayscale and colour image segmentation algorithms. The convincing results of improving the performance of different segmentation algorithms prove the potential of the proposed textural difference enhancement method