Adaptive Image Decomposition Into Cartoon and Texture Parts Optimized by the Orthogonality Criterion

In this paper a new decomposition method is introduced that splits the image into geometric (or cartoon) and texture parts. Following a total variation based preprocesssing, the core of the proposed method is an anisotropic diffusion with an orthogonality based parameter estimation and stopping condition. The quality criterion is defined by the theoretical assumption that the cartoon and the texture components of an image should be orthogonal to each other. The presented method has been compared to other decomposition algorithms through visual and numerical evaluation to prove its superiority

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

Blind Speckle Decorrelation for SAR Image Despeckling

In the past few decades, several methods have been developed for despeckling synthetic aperture radar (SAR) images. A considerable number of them have been derived under the assumption of a fully-developed speckle model in which the multiplicative speckle noise is supposed to be a white process. Unfortunately, the transfer function of SAR acquisition systems can introduce a statistical correlation, which decreases the despeckling efficiency of such filters. In this paper, a whitening method is proposed for processing a complex image acquired by a SAR system. We demonstrate that the proposed approach allows the successful application of classical despeckling algorithms. First, we perform an estimation of the SAR system frequency response based on some statistical properties of the acquired image and by using realistic assumptions. Then, a decorrelation process is applied on the acquired image, taking into account the presence of point targets. Finally, the image is despeckled. The experimental results show that the despeckling filters achieve better performance when they are preceded by the proposed whitening method; furthermore, the radiometric characteristics of the image are preserve

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Speckle Noise Reduction via Homomorphic Elliptical Threshold Rotations in the Complex Wavelet Domain

Many clinicians regard speckle noise as an undesirable artifact in ultrasound images masking the underlying pathology within a patient. Speckle noise is a random interference pattern formed by coherent radiation in a medium containing many sub-resolution scatterers. Speckle has a negative impact on ultrasound images as the texture does not reflect the local echogenicity of the underlying scatterers. Studies have shown that the presence of speckle noise can reduce a physician's ability to detect lesions by a factor of eight. Without speckle, small high-contrast targets, low contrast objects, and image texture can be deduced quite readily. Speckle filtering of medical ultrasound images represents a critical pre-processing step, providing clinicians with enhanced diagnostic ability. Efficient speckle noise removal algorithms may also find applications in real time surgical guidance assemblies. However, it is vital that regions of interests are not compromised during speckle removal. This research pertains to the reduction of speckle noise in ultrasound images while attempting to retain clinical regions of interest. Recently, the advance of wavelet theory has lead to many applications in noise reduction and compression. Upon investigation of these two divergent fields, it was found that the speckle noise tends to rotate an image's homomorphic complex-wavelet coefficients. This work proposes a new speckle reduction filter involving a counter-rotation of these complex-wavelet coefficients to mitigate the presence of speckle noise. Simulations suggest the proposed denoising technique offers superior visual quality, though its signal-to-mean-square-error ratio (S/MSE) is numerically comparable to adaptive frost and kuan filtering. This research improves the quality of ultrasound medical images, leading to improved diagnosis for one of the most popular and cost effective imaging modalities used in clinical medicine