Parallel and pipeline computation of fast unitary transforms

The letter discusses the parallel and pipeline organisation of fast-unitary-transform algorithms such as the fast Fourier transform, and points out the efficiency of a combined parallel-pipeline processor of a transform such as the Haar transform, in which 2n?1 hardware `butterflies? generate a transform of order 2n every computation cycle.     

RAPID PROTOTYPING - Framework for FPGA-based discrete biorthogonal wavelet transforms implementation

The discrete wavelet transform has taken its place at the forefront of research for the development of signal and image processing applications. These wavelet-based approaches have outperformed existing strategies in many areas including telecommunication, numerical analysis and, most notably, image/video compression. The authors present an investigation into the design and implementation of 1-D and 2-D discrete biorthogonal wavelet transforms (DBWTs) using a field programmable gate array (FPGA)-based rapid prototyping environment. The proposed architectures for DBWTs are scalable, modular and have less area and time complexity when compared with existing structures. FPGA implementation results based on a Xilinx Virtex-2000E device have shown that the proposed system provides an efficient solution for the processing of DBWTs in real-time     

Analysis of error in the fixed-point implementation of two-dimensional discrete wavelet transforms

Computational error due to the fixed-point implementation of two-dimensional (2-D) discrete wavelet transform (DWT) is analyzed. This analysis is based on the exact knowledge of the DWT analysis and synthesis filters and the word length of the original image. In the fixed-point implementation, it is crucial to understand and analyze effects of finite precision in filters coefficients as well as rounding of intermediate calculations for the purpose of storage and/or transmission. Analyses and formulations are presented for both convolution and lifting approaches and they are validated by Monte Carlo simulations. The specific example used throughout this work is the lossy wavelet transformation used in the JPEG2000 compression standard.     

Symmetric-extension-compatible reversible integer-to-integer wavelet transforms

Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric extension. One of these families is then studied in detail, and several interesting results concerning its member transforms are presented. In addition, some new reversible ITI structures are derived that are useful in conjunction with techniques like symmetric extension. Last, the relationship between symmetric extension and per-lifting-step extension is explored, and some new results are obtained in this regard.     

Time-varying lapped transforms and wavelet packets

The perfect reconstruction conditions for a time-varying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is developed employing a time varying, tree association of ELTs. In all cases perfect reconstruction is inherently assured     

Discrete inverses for nonorthogonal wavelet transforms

Discrete nonorthogonal wavelet transforms play an important role in signal processing by offering finer resolution in time and scale than their orthogonal counterparts. The standard inversion procedure for such transforms is a finite expansion in terms of the analyzing wavelet. While this approximation works quite well for many signals, it fails to achieve good accuracy or requires an excessive number of scales for others. This paper proposes several algorithms that provide more adequate inversion and compares them in the case of Morlet wavelets. In the process, both practical and theoretical issues for the inversion of nonorthogonal wavelet transforms are discussed     

VLSI architectures for discrete wavelet transforms

A folded architecture and a digit-serial architecture are proposed for implementation of one- and two-dimensional discrete wavelet transforms. In the one-dimensional folded architecture, the computations of all wavelet levels are folded to the same low-pass and high-pass filters. The number of registers in the folded architecture is minimized by the use of a generalized life time analysis. The converter units are synthesized with a minimum number of registers using forward-backward allocation. The advantage of the folded architecture is low latency and its drawbacks are increased hardware area, less than 100% hardware utilization, and the complex routing and interconnection required by the converters used. These drawbacks are eliminated in the alternate digit-serial architecture at the expense of an increase in the system latency and some constraints on the wordlength. In latency-critical applications, the use of the folded architecture is suggested. If latency is not so critical, the digit-serial architecture should be used. The use of a combined folded and digit-serial architecture is proposed for implementation of two-dimensional discrete wavelet transforms     

Time-domain design of low delay wavelet transforms

The authors use a time-domain design methodology previously used for perfect reconstruction filter banks to design wavelet prototypes which may be used to generate the discrete wavelet transform (DWT). An advantage of this method is the significant reduction in the inherent delay, and consequent reduction in the number of multiplications required to implement the DWT. It is proposed that these low delay wavelets will find applications in time critical systems.<>     

The coding gain of multiplexed wavelet transforms

Evangelista (1994, 1993) introduced the multiplexed wavelet transform (MWT) and pointed out its potential applications to the analysis, synthesis, processing and coding of pseudo-periodic signals such as voiced speech and music. Coders based on the MWT have been shown to outperform the conventional subband coders when a reliable pitch parameter can be extracted from data. In this paper, we investigate the effects of uniform quantization of the MWT coefficients. We compare the performance of the new coders with that of WT, block-DCT, and KLT coders in terms of the coding gain achieved when optimal bit allocation schemes are adopted     

A new framework for complex wavelet transforms

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we can exploit this flexibility to create the complex double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3/sup m/-1/2/sup m/-1) in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy.     

基于小波变换的多尺度SSIM算法

提出一种基于小波变换的多尺度结构相似度的图像质量评价(WWMS-SSIM)算法。首先对原始图像和失真图像分别进行小波变换,在对应的低频子带图像中比较亮度和相关度差异,在对应高频子带图像中比较对比度、相关度和结构差异,然后赋予不同子带图像不同的视觉加权值,最后得到归一化的图像质量评价值。通过对不同失真类型图像以及Live数据库图像的评价,证明了提出的算法(WWMS-SSIM)相对均方误差、峰值信噪比、结构相似度以及改进的结构相似度评价算法更符合人类的主观视觉感受。     

Architectures for wavelet transforms: A survey

Wavelet transforms have proven to be useful tools for several applications, including signal analysis, signal compression and numerical analysis. This paper surveys the VLSI architectures that have been proposed for computing the Discrete and Continuous Wavelet Transforms for 1-D and 2-D signals. The architectures are based upon on-line versions of the wavelet transform algorithms. These architectures support single chip implementations and are optimal with respect to both area and time under the word-serial model.     

Multidimensional, mapping-based complex wavelet transforms.

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3M - 1)/(2M - 1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.     

Detection of ECG characteristic points using wavelet transforms

An algorithm based on wavelet transforms (WT's) has been developed for detecting ECG characteristic points. With the multiscale feature of WT's, the QRS complex can be distinguished from high P or T waves, noise, baseline drift, and artifacts. The relation between the characteristic points of ECG signal and those of modulus maximum pairs of its WT's is illustrated. By using this method, the detection rate of QRS complexes is above 99.8% for the MIT/BIH database and the P and T waves can also be detected, even with serious base line drift and noise     

Folded multiplierless lifting-based wavelet pipeline

A folded multiplierless lifting-based wavelet pipeline for 9/7 and 5/3 filters is presented. The proposed pipeline requires a small amount of logic and achieves a 100% hardware utilisation with a performance loss lower than 0.7 dB compared to a JPEG2000 compliant wavelet stage     

Analysis and implementation of morphological skeleton transforms

This paper presents the analysis and the implementation algorithms of the morphological skeleton transform (MST) of binary images. A general MST algorithm is provided from which different subclasses of MSTs can be derived by choosing different structuring elements. Three subclasses of MSTs are discussed in this paper: the uniform-step-distance MST (USDMST), the periodically-uniform-step-distance MST (PUSDMST) and the pseudo-Euclidean MST (PEMST). A general discrete distance called morphological distance relates distance measures to the definitions of structuring elements. The PEMST is proposed which uses isotropic discrete structuring elements called quasi-circular structuring elements (QCSE). The QCSEs of all integer sizes are composed by a dilation interpolation method so that they can be decomposed into simplest elements in order to reduce computation. The PEMST has better performance in terms of rotation-invariance than any existing MSTs. The algorithm has an approximately linear computational complexity. Finally, the implementation of the three MSTs are discussed.     

Cyclic wavelet transforms for arbitrary finite data lengths

Multiresolution analysis via decomposition into wavelets has been established as an important transform technique in signal processing. A wealth of results is available on this subject, and particularly, the framework has been extended to treat finite length sequences of size 2ⁿ (for positive integers n) over finite fields. The present paper extends this idea further to provide a framework for dealing with arbitrary finite data lengths. This generalization is largely motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Here we extend the previous two-band formulation of the transform to treat a p-band case in general (i.e. for data length pⁿ), where p is a prime number, and we also give a general result for developing transforms over composite-length sequences. Potential applications and computational complexity issues are discussed as well.     

Nonlinear wavelet transforms for image coding via lifting

We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.     

Directional dyadic wavelet transforms: design and algorithms

We propose a simple and efficient technique for designing translation invariant dyadic wavelet transforms (DWTs) in two dimensions. Our technique relies on an extension of the work of Duval-Destin et al. (1993) where dyadic decompositions are constructed starting from the continuous wavelet transform. The main advantage of this framework is that it allows for a lot of freedom in designing two-dimensional (2-D) dyadic wavelets. We use this property to construct directional wavelets, whose orientation filtering capabilities are very important in image processing. We address the efficient implementation of these decompositions by constructing approximate QMFs through an L (2) optimization. We also propose and study an efficient implementation in the Fourier domain for dealing with large filters.