Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

A DWT based perceptual video coding framework: concepts, issues and techniques

The work in this thesis explore the DWT based video coding by the introduction of a novel DWT (Discrete Wavelet Transform) / MC (Motion Compensation) / DPCM (Differential Pulse Code Modulation) video coding framework, which adopts the EBCOT as the coding engine for both the intra- and the inter-frame coder. The adaptive switching mechanism between the frame/field coding modes is investigated for this coding framework. The Low-Band-Shift (LBS) is employed for the MC in the DWT domain. The LBS based MC is proven to provide consistent improvement on the Peak Signal-to-Noise Ratio (PSNR) of the coded video over the simple Wavelet Tree (WT) based MC. The Adaptive Arithmetic Coding (AAC) is adopted to code the motion information. The context set of the Adaptive Binary Arithmetic Coding (ABAC) for the inter-frame data is redesigned based on the statistical analysis. To further improve the perceived picture quality, a Perceptual Distortion Measure (PDM) based on human vision model is used for the EBCOT of the intra-frame coder. A visibility assessment of the quantization error of various subbands in the DWT domain is performed through subjective tests. In summary, all these findings have solved the issues originated from the proposed perceptual video coding framework. They include: a working DWT/MC/DPCM video coding framework with superior coding efficiency on sequences with translational or head-shoulder motion; an adaptive switching mechanism between frame and field coding mode; an effective LBS based MC scheme in the DWT domain; a methodology of the context design for entropy coding of the inter-frame data; a PDM which replaces the MSE inside the EBCOT coding engine for the intra-frame coder, which provides improvement on the perceived quality of intra-frames; a visibility assessment to the quantization errors in the DWT domain

Learning-based Wavelet-like Transforms For Fully Scalable and Accessible Image Compression

The goal of this thesis is to improve the existing wavelet transform with the aid of machine learning techniques, so as to enhance coding efficiency of wavelet-based image compression frameworks, such as JPEG 2000. In this thesis, we first propose to augment the conventional base wavelet transform with two additional learned lifting steps -- a high-to-low step followed by a low-to-high step. The high-to-low step suppresses aliasing in the low-pass band by using the detail bands at the same resolution, while the low-to-high step aims to further remove redundancy from detail bands by using the corresponding low-pass band. These two additional steps reduce redundancy (notably aliasing information) amongst the wavelet subbands, and also improve the visual quality of reconstructed images at reduced resolutions. To train these two networks in an end-to-end fashion, we develop a backward annealing approach to overcome the non-differentiability of the quantization and cost functions during back-propagation. Importantly, the two additional networks share a common architecture, named a proposal-opacity topology, which is inspired and guided by a specific theoretical argument related to geometric flow. This particular network topology is compact and with limited non-linearities, allowing a fully scalable system; one pair of trained network parameters are applied for all levels of decomposition and for all bit-rates of interest. By employing the additional lifting networks within the JPEG2000 image coding standard, we can achieve up to 17.4% average BD bit-rate saving over a wide range of bit-rates, while retaining the quality and resolution scalability features of JPEG2000. Built upon the success of the high-to-low and low-to-high steps, we then study more broadly the extension of neural networks to all lifting steps that correspond to the base wavelet transform. The purpose of this comprehensive study is to understand what is the most effective way to develop learned wavelet-like transforms for highly scalable and accessible image compression. Specifically, we examine the impact of the number of learned lifting steps, the number of layers and the number of channels in each learned lifting network, and kernel support in each layer. To facilitate the study, we develop a generic training methodology that is simultaneously appropriate to all lifting structures considered. Experimental results ultimately suggest that to improve the existing wavelet transform, it is more profitable to augment a larger wavelet transform with more diverse high-to-low and low-to-high steps, rather than developing deep fully learned lifting structures

Application of Stochastic Diffusion for Hiding High Fidelity Encrypted Images

Cryptography coupled with information hiding has received increased attention in recent years and has become a major research theme because of the importance of protecting encrypted information in any Electronic Data Interchange system in a way that is both discrete and covert. One of the essential limitations in any cryptography system is that the encrypted data provides an indication on its importance which arouses suspicion and makes it vulnerable to attack. Information hiding of Steganography provides a potential solution to this issue by making the data imperceptible, the security of the hidden information being a threat only if its existence is detected through Steganalysis. This paper focuses on a study methods for hiding encrypted information, specifically, methods that encrypt data before embedding in host data where the ‘data’ is in the form of a full colour digital image. Such methods provide a greater level of data security especially when the information is to be submitted over the Internet, for example, since a potential attacker needs to first detect, then extract and then decrypt the embedded data in order to recover the original information. After providing an extensive survey of the current methods available, we present a new method of encrypting and then hiding full colour images in three full colour host images with out loss of fidelity following data extraction and decryption. The application of this technique, which is based on a technique called ‘Stochastic Diffusion’ are wide ranging and include covert image information interchange, digital image authentication, video authentication, copyright protection and digital rights management of image data in general