一种DWT的提升实现及其图像编码应用

根据多项式矩阵的初等变换理论,把一种有理滤波器系数17/11双正交小波对应的DWT分解为提升步骤,极大地降低了计算复杂度.最后,将此提升小波变换应用于嵌入式图像编码.实验表明,其图像压缩性能显著超过JPEG 2000标准中采用的9/7提升小波变换.     

基于双正交小波变换的航空图像压缩研究

提出一种基于提升方案的双正交小波变换结合SPIHT编码的图像压缩方法.小波提升方案是继多分辨分析之后,另一种非常有效的构造小波滤波器的方法,在双正交条件下按所需的小波性能自由构造双正交小波基,并能加快小波变换的执行速度.分析了应用提升方案构造双正交小波的算法,选用性能优良的双正交小波,结合SPIHT编码,进行图像压缩.实验表明,通过该方法进行图像压缩,图像重建质量较高.     

航空图像压缩的双正交小波滤波器整数化设计

在航空图像压缩中,通常采用具有线性相位、正则性、消失矩和完全重构,及适于硬件实现、实时等特性的小波。根据小波滤波器设计,提出了一种基于图像压缩的构造整数双正交小波滤波器的设计方法。从选择小波基的原则为出发点,以CDF9-7小波基为参考,以压缩效果为准则来构造出更优的双正交整数小波基,并且采用航空图像为标准训练图像,以压缩比、峰值信噪比、压缩后保留能量百分比为参数,来寻找最优的小波基。试验结果证明,此方法可以实施非常简单的、无浮点乘法的运算,因而减少运算复杂性以及降低小波硬件实现的难度。     

提升格式的小波变换及在视频压缩中的应用

提升方法是计算离散小波变换的有效手段，将提升三维小波变换用于视频信号压缩。时间方向小渡变换选用Haar滤波器组，空间小波变换则在常规的图像编码所常用的D9/7滤波器组基础上，对其参数进行调整，进一步减少运算量。实验表明这种调整取得了与D9/7双正交小波基本一致图像编码效果，但提高了运算速度。     

Q-shift复小波的一种新型构造方法及其在图像去噪中的应用

为了提高复小波变换的效率,本文提出了一种设计Q-shift复小波滤波器的新方法。与目前采用多相位矩阵的晶格分解结构得到正交小波的方法不同的是,这里从更为一般的完全重构滤波器组出发寻求满足特定要求的正交小波。不但可以构造出系数更为简单、运算更加方便的小波,而且可以实现任意精度的复小波变换。该方法的可拓展性好,可以很方便的添加如高阶消失矩等限制并简化设计过程。以普遍采用的Q-shift10/10小波为例,利用本文构造的正交小波可将复小波变换中的乘法运算降低到原来的1/3,而加法基本相当,且小波的频率选择性质更好。将其用于图像去噪的实验表明,采用本文构造的小波可以显著提高处理速度并得到更高的峰值信噪比(PSNR)。     

基于双正交FDWT的雷达数据压缩和目标识别方法

本文由双正交共轭滤波器构造有限维内积空间的双正交多分辨分析和快速离散小波变换(FDWT),提出信号的对偶小波变换方法,并将其用于降低雷达数据存储量,提出双正交变换系数筛选方法以及基于压缩数据的小波域相关和最小距离分类方法。通过六种飞机目标的距离高分辨数据的分类实验,证明本文提出的变换、压缩和识别方法是有效的。     

紧支集双正交小波及其对应的FIR滤波器的一种构造方法

给出了一种利用Ｂ样条构造具有线性相位的紧支集对偶尺度函数，对应的紧支集双正交小波及其相应的ＦＩＲ滤波器组的方法。     

对称—反对称多小波滤波器组的参数化构造及其在图像压缩中的应用

本文给出了一类对称—反对称多小波滤波器组参数化设计方法,并在此基础上提出了新的多小波零树编码方案.实验表明,与常用的9-7单小波相比,我们所设计的双正交对称—反对称多小波可使编码性能有较大幅度的改善.     

具有任意正则阶的M-带对称正交小波设计

利用计算代数中Grobner基与合冲模的概念与算法,论文提出了一种多相位矩阵的正交化方法,在此基础上得到了同时具有对称性和任意正则阶的M-带正交小波的高效设计方法.克服了现有算法构造过程复杂以及不能保持线性相位的缺陷,另外,当所求得的尺度滤波器系数为参数形式时,本文算法求得的小波滤波器也为含参数的,因而可以根据实际问题灵活选取适当参数从而得到所需要的M-带小波系统.     

一类易于VLSI实现的对称双正交小波设计方法研究

该文提出了一类对称双正交小波的设计方法。该类双正交小波的小波滤波器组具有格形结构,实现该小波变换的分析滤波器组和综合滤波器组满足双正交条件和正则性条件,且设计的各滤波器均为实数二进制系数,因而该小波变换易于高速VLSI实现。文中的理论推导和设计实例,均验证了该设计方法的有效性。     

Parametrization construction of biorthogonal wavelet filter banks for image coding

We construct popular biorthogonal wavelet filter banks (BWFBs) having the linear phase and arbitrary multiplicity of vanishing moments (VMs). A novel parametrization construction technique, which is based on the theory of Diophantine equation, is presented and explicit one-parameter expressions of the BWFBs are derived. Using the expressions, any one-parameter family of BWFBs with different VMs can be constructed, and ten families, i.e., 5/7, 6/6, 9/7, 6/10, 5/11, 10/6, 13/7, 6/14, 17/11, and 10/18 families, are constructed here. The free parameter can be used to optimize the resulting BWFBs with respect to other criteria. In particular, in each family, three specific BWFBs with attractive features are obtained by adjusting the free parameter: the first has optimum coding gain and rational coefficients; the second which also has rational coefficients is very close to a quadrature mirror filter (QMF) bank; and the third which has binary coefficients can realize a multiplication-free discrete wavelet transform. In addition, four BWFBs are systematically verified to exhibit performance competitive to several state-of-the-art BWFBs for image compression, and yet require lower computational costs. This work was supported by the National Natural Science Foundation of China under Grant 60021302     

Construction of parametric biorthogonal wavelet filter banks with two parameters for image coding

We had presented a simple technique, which is based on the theory of Diophantine equation, for parametrization of popular biorthogonal wavelet filter banks (BWFBs) having the linear phase and arbitrary multiplicity of vanishing moments (VMs), and constructed a type of parametric BWFBs with one free parameter [15]. Here we generalize this technique to the case of two parameters, and construct a type of parametric BWFBs with two free parameters. The closed-form parameter expressions of the BWFBs are derived, with which any two-parameter family of BWFBs having preassigned VMs can be constructed, and six families, i.e., 9/11, 10/10, 13/11, 10/14, 17/11, and 10/18 families, are considered here. Two parameters provide two degrees of freedom to optimize the resulting BWFBs with respect to other criteria. In particular, in each family, three specific rational-coefficient BWFBs with attractive features are obtained by adjusting the parameters: the first is not only very close to a quadrature mirror filter (QMF) bank, but has optimum coding gain; the second possesses characteristics that are close to the irrational BWFB with maximum VMs by Cohen et al.; and the last which has binary coefficients can realize a multiplication-free discrete wavelet transform. In addition, two BWFBs are systematically verified to exhibit performance competitive to several state-of-the-art BWFBs for image compression, and yet require lower computational costs. This work was supported by the Natural Science Foundation of Jiangsu province, China under Grant 07KJD520005.     

Biorthogonal nearly coiflet wavelets for image compression

Filter bank design for wavelet compression is crucial; careful design enables superior quality for broad classes of images. The Bernstein basis for frequency-domain construction of biorthogonal nearly coiflet (BNC) wavelet bases forms a unified design framework for high-performance medium-length filters. A common filter bandwidth is characteristic of widely favoured BNC filter pairs: the classical CDF 9/7, the Villasenor 6/10, and the Villasenor 10/18. Based on this observation, we construct previously unknown BNC 17/11 and BNC 16/8 wavelet filters. Key filter-quality evaluation metrics, due to Villasenor, demonstrate these filters to be well suited for image compression. Also studied are the biorthogonal coiflet 17/11 (half-band), 18/10 and 10/6 filter pairs, which have not previously been formally evaluated for image coding. Simulation results confirm that the BNC 17/11 and BNC 16/8 wavelet bases are outstanding for compression of natural and medical images, and particularly for images with significant high-frequency detail, such as fingerprints. The BNC 17/11 pair recommends itself for international standardization for the compression of still images; the BNC 16/8 pair for high-quality compression of production quality video. Experimental evidence suggests biorthogonal filters achieve good compression if, subject to a filter bandwidth constraint, maximum vanishing moments are obtained for a given filter support.     

A New Design Method of 9-7 Biorthogonal Filter Banks Based on Odd Harmonic Function

The floating-point implementation of a CDF-9-7 wavelet transform with irrational coefficients on a resource limited hardware platform is a challenging task. This paper presents a new design method of 9-7 biorthogonal wavelet filter bank (FB) based on classical Fourier theory, the so-called odd harmonic function (OHF) analysis. Three types of binary rational 9-7 biorthogonal wavelet FBs have been derived, considering vanishing moments in addition to the rationality of filter coefficients. The extensive experiments for the implementation of the new design on the SPIHT (Set Partitioning In Hierarchical Trees) platform have been conducted and the results show that the performance of the proposed new biorthogonal FBs is equal to, or in several cases outperforms the, CDF-9-7 FB.     

Wavelet filter evaluation for image compression

Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2(L),2(L)). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design.     

Design of multiplierless, high-performance, wavelet filter banks with image compression applications

The JPEG2000 image coding standard employs the biorthogonal 9/7 wavelet for lossy compression. The performance of a hardware implementation of the 9/7 filter bank depends on the accuracy and the efficiency with which the quantized filter coefficients are represented. A high-precision representation ensures compression performance close to the unquantized, infinite precision filter bank, but at the cost of increased hardware resources and processing time. If the filter coefficients are quantized such that the filter bank properties are preserved, then, the degradation in compression performance will be minimal. This paper investigates two filter structures and two "compensating" filter coefficient quantization methods for improving the performance of multiplierless, quantized filter banks. Rather than using an optimization technique to guide the design process, the new methods utilizes the perfect reconstruction requirements of the filter bank. The results indicate that the best method (a cascade structure with compensating zeros) realizes image-compression performance very similar to the unquantized filter case while also achieving a fast, efficient hardware implementation.     

Optimization Design of Biorthogonal Wavelet Filter Banks for Extending JPEG 2000 Standard Part-2

A generic optimization design approach of biorthogonal wavelet filter banks (BWFB) for extending the JPEG 2000 standard part-2 is presented in this paper. This approach adopts Vaidyanathan optimal coding gain criterion to design the BWFB, and adopts peak signal-to-noise ratio (PSNR) as the criterion to optimize this BWFB. A functional relation between the general BWFB and their lifting scheme is derived in the first place with respect to one free variable, so that the optimization design of the BWFB is easier and more convenient. In addition, a general image model is formulated as a first-order Markov process driven by Gaussian white noise. It is taken as an input of two-channel filter banks which satisfy perfect reconstruction (PR) condition to realize subband coding for obtaining the optimal BWFB according to the Vaidyanathan optimal coding gain criterion. Finally, a new 9/7 BWFB with rational coefficients is proposed for extending the JPEG 2000 standard part-2, with PSNR of reconstructed images only 0.20 dB lower than standard CDF 9/7 BWFB for infrared thermal image compressions.     

Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

Complex, linear-phase filters for efficient image coding

With the exception of the Haar basis, real-valued orthogonal wavelet filter banks with compact support lack symmetry and therefore do not possess linear phase. This has led to the use of biorthogonal filters for coding of images and other multidimensional data. There are, however, complex solutions permitting the construction of compactly supported, orthogonal linear phase QMF filter banks. By explicitly seeking solutions in which the imaginary part of the filter coefficients is small enough to be approximated to zero, real symmetric filters can be obtained that achieve excellent compression performance     

Efficient Block-Based Frequency Domain Wavelet Transform Implementations

Subband decompositions for image coding have been explored extensively over the last few decades. The condensed wavelet packet (CWP) transform is one such decomposition that was recently shown to have coding performance advantages over conventional decompositions. A special feature of the CWP is that its design and implementation are performed in the cyclic frequency domain. While performance gains have been reported, efficient implementations of the CWP (or more generally, efficient implementations of cyclic filter banks) have not yet been fully explored. In this paper, we present efficient block-based implementations of cyclic filter banks along with an analysis of the arithmetic complexity. Block-based cyclic filter bank implementations of the CWP coder are compared with conventional subband/wavelet image coders whose filter banks are implemented in the time domain. It is shown that block-based cyclic filter bank implementations can result in CWP coding systems that outperform the popular image coding systems both in terms of arithmetic complexity and coding performance.