New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al. The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods. © 2004 IEEE.published_or_final_versio

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

In this paper, a new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filterbanks are parameterized by two functions (β(z) and α(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical β(z) and α(z) was considered by Phoong et al. with the delay parameter M chosen as 2N - 1. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase constraint is relaxed, the lengths of β(z) and α(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.published_or_final_versio

Ubiquitous Scalable Graphics: An End-to-End Framework using Wavelets

Advances in ubiquitous displays and wireless communications have fueled the emergence of exciting mobile graphics applications including 3D virtual product catalogs, 3D maps, security monitoring systems and mobile games. Current trends that use cameras to capture geometry, material reflectance and other graphics elements means that very high resolution inputs is accessible to render extremely photorealistic scenes. However, captured graphics content can be many gigabytes in size, and must be simplified before they can be used on small mobile devices, which have limited resources, such as memory, screen size and battery energy. Scaling and converting graphics content to a suitable rendering format involves running several software tools, and selecting the best resolution for target mobile device is often done by trial and error, which all takes time. Wireless errors can also affect transmitted content and aggressive compression is needed for low-bandwidth wireless networks. Most rendering algorithms are currently optimized for visual realism and speed, but are not resource or energy efficient on mobile device. This dissertation focuses on the improvement of rendering performance by reducing the impacts of these problems with UbiWave, an end-to-end Framework to enable real time mobile access to high resolution graphics using wavelets. The framework tackles the issues including simplification, transmission, and resource efficient rendering of graphics content on mobile device based on wavelets by utilizing 1) a Perceptual Error Metric (PoI) for automatically computing the best resolution of graphics content for a given mobile display to eliminate guesswork and save resources, 2) Unequal Error Protection (UEP) to improve the resilience to wireless errors, 3) an Energy-efficient Adaptive Real-time Rendering (EARR) heuristic to balance energy consumption, rendering speed and image quality and 4) an Energy-efficient Streaming Technique. The results facilitate a new class of mobile graphics application which can gracefully adapt the lowest acceptable rendering resolution to the wireless network conditions and the availability of resources and battery energy on mobile device adaptively

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Linear Unmixing of Hyperspectral Signals via Wavelet Feature Extraction

A pixel in remotely sensed hyperspectral imagery is typically a mixture of multiple electromagnetic radiances from various ground cover materials. Spectral unmixing is a quantitative analysis procedure used to recognize constituent ground cover materials (or endmembers) and obtain their mixing proportions (or abundances) from a mixed pixel. The abundances are typically estimated using the least squares estimation (LSE) method based on the linear mixture model (LMM). This dissertation provides a complete investigation on how the use of appropriate features can improve the LSE of endmember abundances using remotely sensed hyperspectral signals. The dissertation shows how features based on signal classification approaches, such as discrete wavelet transform (DWT), outperform features based on conventional signal representation methods for dimensionality reduction, such as principal component analysis (PCA), for the LSE of endmember abundances. Both experimental and theoretical analyses are reported in the dissertation. A DWT-based linear unmixing system is designed specially for the abundance estimation. The system utilizes the DWT as a pre-processing step for the feature extraction. Based on DWT-based features, the system utilizes the constrained LSE for the abundance estimation. Experimental results show that the use of DWT-based features reduces the abundance estimation deviation by 30-50% on average, as compared to the use of original hyperspectral signals or conventional PCA-based features. Based on the LMM and the LSE method, a series of theoretical analyses are derived to reveal the fundamental reasons why the use of the appropriate features, such as DWT-based features, can improve the LSE of endmember abundances. Under reasonable assumptions, the dissertation derives a generalized mathematical relationship between the abundance estimation error and the endmember separabilty. It is proven that the abundance estimation error can be reduced through increasing the endmember separability. The use of DWT-based features provides a potential to increase the endmember separability, and consequently improves the LSE of endmember abundances. The stability of the LSE of endmember abundances is also analyzed using the concept of the condition number. Analysis results show that the use of DWT-based features not only improves the LSE of endmember abundances, but also improves the LSE stability

Learning Sparse Orthogonal Wavelet Filters

The wavelet transform is a well studied and understood analysis technique used in signal processing. In wavelet analysis, signals are represented by a sum of self-similar wavelet and scaling functions. Typically, the wavelet transform makes use of a fixed set of wavelet functions that are analytically derived. We propose a method for learning wavelet functions directly from data. We impose an orthogonality constraint on the functions so that the learned wavelets can be used to perform both analysis and synthesis. We accomplish this by using gradient descent and leveraging existing automatic differentiation frameworks. Our learned wavelets are able to capture the structure of the data by exploiting sparsity. We show that the learned wavelets have similar structure to traditional wavelets. Machine learning has proven to be a powerful tool in signal processing and computer vision. Recently, neural networks have become a popular and successful method used to solve a variety of tasks. However, much of the success is not well understood, and the neural network models are often treated as black boxes. This thesis provides insight into the structure of neural networks. In particular, we consider the connection between convolutional neural networks and multiresolution analysis. We show that the wavelet transform shares similarities to current convolutional neural network architectures. We hope that viewing neural networks through the lens of multiresolution analysis may provide some useful insights. We begin the thesis by motivating our method for one-dimensional signals. We then show that we can easily extend the framework to multidimensional signals. Our learning method is evaluated on a variety of supervised and unsupervised tasks, such as image compression and audio classification. The tasks are chosen to compare the usefulness of the learned wavelets to traditional wavelets, as well as provide a comparison to existing neural network architectures. The wavelet transform used in this thesis has some drawbacks and limitations, caused in part by the fact that we make use of separable real filters. We address these shortcomings by exploring an extension of the wavelet transform known as the dual-tree complex wavelet transform. Our wavelet learning model is extended into the dual-tree domain with few modifications, overcoming the limitations of our standard model. With this new model we are able to show that localized, oriented filters arise from natural images

Scalable video compression with optimized visual performance and random accessibility

This thesis is concerned with maximizing the coding efficiency, random accessibility and visual performance of scalable compressed video. The unifying theme behind this work is the use of finely embedded localized coding structures, which govern the extent to which these goals may be jointly achieved. The first part focuses on scalable volumetric image compression. We investigate 3D transform and coding techniques which exploit inter-slice statistical redundancies without compromising slice accessibility. Our study shows that the motion-compensated temporal discrete wavelet transform (MC-TDWT) practically achieves an upper bound to the compression efficiency of slice transforms. From a video coding perspective, we find that most of the coding gain is attributed to offsetting the learning penalty in adaptive arithmetic coding through 3D code-block extension, rather than inter-frame context modelling. The second aspect of this thesis examines random accessibility. Accessibility refers to the ease with which a region of interest is accessed (subband samples needed for reconstruction are retrieved) from a compressed video bitstream, subject to spatiotemporal code-block constraints. We investigate the fundamental implications of motion compensation for random access efficiency and the compression performance of scalable interactive video. We demonstrate that inclusion of motion compensation operators within the lifting steps of a temporal subband transform incurs a random access penalty which depends on the characteristics of the motion field. The final aspect of this thesis aims to minimize the perceptual impact of visible distortion in scalable reconstructed video. We present a visual optimization strategy based on distortion scaling which raises the distortion-length slope of perceptually significant samples. This alters the codestream embedding order during post-compression rate-distortion optimization, thus allowing visually sensitive sites to be encoded with higher fidelity at a given bit-rate. For visual sensitivity analysis, we propose a contrast perception model that incorporates an adaptive masking slope. This versatile feature provides a context which models perceptual significance. It enables scene structures that otherwise suffer significant degradation to be preserved at lower bit-rates. The novelty in our approach derives from a set of "perceptual mappings" which account for quantization noise shaping effects induced by motion-compensated temporal synthesis. The proposed technique reduces wavelet compression artefacts and improves the perceptual quality of video