Isotropic polyharmonic B-splines: scaling functions and wavelets.

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-splines do not converge to a Gaussian as the order parameter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more isotropic localization operator that guarantees this convergence, resulting into the isotropic polyharmonic B-splines. Next, we focus on the two-dimensional quincunx subsampling scheme. This configuration is of particular interest for image processing because it yields a finer scale progression than the standard dyadic approach. However, up until now, the design of appropriate filters for the quincunx scheme has mainly been done using the McClellan transform. In our approach, we start from the scaling functions, which are the polyharmonic B-splines and, as such, explicitly known, and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi-orthogonal wavelet transform; e.g., orthonormal, B-spline, and dual. The filters are automatically specified by the scaling relations satisfied by these functions. We prove that the isotropic polyharmonic B-spline wavelet converges to a combination of four Gabor atoms, which are well separated in the frequency domain. We also show that these wavelets are nearly isotropic and that they behave as an iterated Laplacian operator at low frequencies. We describe an efficient fast Fourier transform-based implementation of the discrete wavelet transform based on polyharmonic B-splines.     

Decorrelating scaling functions for wavelet transformations

A method for synthesizing a mask for a scaling equation with allowance for an a priori given correlation function of the noise component is developed. Two biorthogonal basis functions are generated, with a rational mask contained in one of them. Practical algorithms for calculating the mask coefficients are constructed using the modifications of the known orthogonal scaling functions. The results are confirmed by the examples for two types of correlation functions: an exponential function and its B-spline approximation.     

Dual Gabor frames: theory and computational aspects

We consider a general method for constructing dual Gabor elements different from the canonical dual. Our approach is based on combining two Gabor frames such that the generated frame-type operator S/sub g,/spl gamma// is nonsingular. We provide necessary and sufficient conditions on the Gabor window functions g and /spl gamma/ such that S/sub g,/spl gamma// is nonsingular for rational oversampling, considering both the continuous-time and the discrete-time settings. In contrast to the frame operator, the operator S/sub g,/spl gamma// is, in general, not positive. Therefore, all results in Gabor analysis that are based on the positivity of the frame operator cannot be applied directly. The advantage of the proposed characterization is that the algebraic system for computing the Gabor dual elements preserves the high structure of usual Gabor frames, leading to computationally efficient algorithms. In particular, we consider examples in which both the condition number and the computational complexity in computing the proposed dual Gabor elements decrease in comparison to the canonical dual Gabor elements.     

基于Gabor小波变换的彩色图像分割

本文提出了一种基于Gabor小波变换的彩色图像分割方法，首先对彩色图像进行Gabor小波变换，然后进行特征提取，并采用动态聚类K-均值算法进行分类，最后得到图像分割的结果。实验和分析表明，该方法对于彩色自然图像的分割具有较好的效果。     

基于Gabor小波的人脸表情特征提取研究

为了使计算机能更好的识别人脸表情,对基于Gabor小波变换的人脸表情识别方法进行了研究。首先对包含表情区域的静态灰度图像进行预处理,包括对确定的人脸表情区域进行尺寸和灰度归一化,然后利用二维Gabor小波变换提取脸部表情特征,使用快速PCA方法对提取的Gabor小波特征初步降维。再在低维的空间中,利用Fisher准则提取那些有利于分类的特征,最后用SVM分类器进行分类。实验结果表明,上述提出的方法比传统的方法识别速度更快,能达到实时性的要求,并且具有很好的鲁棒性,识别率高。     

基于Gabor小波和支持向量机的人脸识别方法

基于Gabor小波在图像表征方面的优越性,提出了将Gabor小波和支持向量机(SVM)相结合用于人脸识别的方案。用Gabor小波对人脸图像进行特征提取,再利用SVM策略对特征向量进行分类识别,实验的仿真结果验证了本算法的有效性。     

Sparse overcomplete Gabor wavelet representation based on local competitions.

Gabor representations present a number of interesting properties despite the fact that the basis functions are nonorthogonal and provide an overcomplete representation or a nonexact reconstruction. Overcompleteness involves an expansion of the number of coefficients in the transform domain and induces a redundancy that can be further reduced through computational costly iterative algorithms like Matching Pursuit. Here, a biologically plausible algorithm based on competitions between neighboring coefficients is employed for adaptively representing any source image by a selected subset of Gabor functions. This scheme involves a sharper edge localization and a significant reduction of the information redundancy, while, at the same time, the reconstruction quality is preserved. The method is characterized by its biological plausibility and promising results, but it still requires a more in depth theoretical analysis for completing its validation.     

Family of scaling chirp functions, diffraction, and holography

It is observed that diffraction is a convolution operation with a chirp kernel whose argument is scaled. Family of functions obtained from a prototype by shifting and argument scaling form the essential ground for wavelet framework. Therefore, a connection between diffraction and wavelet transform is developed. However, wavelet transform is essentially prescribed for time-frequency and/or multiresolution analysis which is irrelevant in our case. Instead, the proposed framework is useful in various location-depth type of analysis in imaging. The linear transform when the analyzing functions are the chirps is called the scaling chirp transform. The scaled chirp functions do not satisfy the commonly used admissibility condition for wavelets. However, it is formally shown that these neither band nor time limited signals can be used as wavelet functions and the inversion is still possible. Diffraction and in-line holography are revisited within the scaling chirp transform context. It is formally proven that a volume in-line hologram gives perfect reconstruction. The developed framework for wave propagation based phenomena has the potential of advancing both signal processing and optical applications     

Gabor小波变换与图像分块的人脸识别算法研究

以二维Gabor小波变换提取人脸图像特征作为全局特征,对图像进行不等分块,人脸图像区域所在块加大权重,并提取每个子块的特征作为局部特征,对全局特征结合局部特征采用DCT进行降维处理,用支持向量机分类模型进行人脸识别。实验表明:与较同等分块的识别算法相比,该算法可提高人脸识别率。     

Supervised bilateral two-dimensional locality preserving projection algorithm based on Gabor wavelet

Bilateral two-dimensional locality preserving projection (B2DLPP) is an effective method for unsupervised linear dimensionality reduction, which directly extracts face features from image matrices based on locality criterion. Motivated by B2DLPP, this paper proposes a supervised bilateral two-dimensional locality preserving projection (SB2DLPP). Different from B2DLPP, the proposed method takes into account the class information when constructing the similarity matrix. It increases inter-class distance in the projection space so that better right and left-projection matrices are obtained. Furthermore, a Gabor-based supervised bilateral two-dimensional locality preserving projection method is proposed for face recognition. Gabor wavelet representations are adopted for face images to make the proposed method robust to illumination variations and facial expression changes. Then, SB2DLPP is applied to reduce feature dimension. The performance of the proposed method is evaluated and compared with other traditional face recognition schemes on the FERET, Yale and JAFFE databases. The experiment results demonstrate the effectiveness and superiority of the proposed approach.     

线算子引导Gabor小波的视网膜血管分割

视网膜血管自动分割能辅助诊断某些眼底疾病和系统性血管疾病。为了提高血管自动分割的效率,因此提出了一种线算子引导Gabor小波的视网膜血管分割方法。利用线算子检测血管方向的最优匹配角,将其作为Gabor小波变换的旋转角构建4个不同尺度的Gabor小波,并提取4维Gabor小波特征,加上两个线强度和预处理后的图像灰度,构建7维特征向量,采用SVM进行分类。与其他基于Gabor小波的方法相比,本方法只需计算最优匹配角所对应方向的Gabor小波特征,大大降低了多尺度Gabor小波特征提取的计算量,此外线算子特征与Gabor小波特征的良好互补性,有利于提高血管与背景的辨别度。在DRIVE眼底数据库上进行实验,其平均准确率、灵敏度及特异性分别为0. 936 1、0. 823 8及0. 955 4,获得了不错的分割性能。     

Fast, accurate interpolation with B-spline scaling functions

A new method for interpolation using B-spline scaling functions is presented which provides significant advantages compared with previously published approaches using the FFT or DST. Periodisation of the sequence is avoided and constraints on the boundary conditions are relaxed. A simple algorithm is given which yields high accuracy with lower computational complexity than FFT or DST techniques     

基于Gabor小波和HSV水污染植物检测

以水葫芦的水生植物入侵严重影响环境,现阶段的河流污染监测仍然停留在人工检测视频监控,文中对视频设备所收集的图像,经过高斯滤波进行图像预处理去除噪声之后,运用二维Gabor小波纹理特征提取相关特征值,运用HSV颜色空间提取相关颜色特征值,结合设定的相关参考阈值,在污染面积计算方面体现出良好性能。     

利用小波变换与Gabor滤波检测红外小目标

将小波变换应用于红外图像,提出了一种新的弱小目标检测方法。该算法首先对图像进行小波变换。为了获取图像的多方向性分解,使用Gabor滤波器与高频信号做卷积运算得到24个方向的高频信息。计算各点的局部能量以及方向离散值,将以上特征融合,得到图像的多特征统计值。其次采用Renyi信息熵分割完成目标检测。最后,由于卷积运算,将会造成弱小目标点的扩大。因此,利用检测结果中小目标具有较大面积的特点,有效地排除了虚警。实验结果表明,该算法参数较少,能较精确地检测出红外弱小目标。     

Note on the transform property of band-limited functions

Some comments and elaborations are made with reference to a recent contribution by Erteza and Lin [1] on sampling low-pass deterministic signals. It is shown that the expansion theorem of the Erteza-Lin paper involves an incomplete set of orthogonal functions and consequently lacks the generality claimed for it.     

Optimum discrete wavelet scaling and its application to delay andDoppler estimation

This paper studies the scaling of an arbitrary waveform from its samples. The scaling problem is formulated as a mean-square minimization, and the resulting estimator consists of two parts: noise filtering and sinc function scaling. Sinc function scaling is a time-dependent process and requires O(N²) operations, where N is the data length. A fast algorithm based on the FFT is proposed to reduce the complexity to O(Nlog₂N). This new algorithm is applied to wideband time delay and Doppler estimation, where the optimum wavelet is one of the received signal samples that has no analytic form. The scaling method is found to be very effective in that the estimation accuracy achieves the Cramer-Rao lower bound (CRLB)     

小波阈值函数算法的实现及比较

随着小波理论的日益完善,小波阈值降噪已经得到越来越广泛的应用.小波阈值降噪中,阈值函数的算法直接影响降噪效果.首先讨论了小波阈值降噪的基本原理;其次通过理论分析和MATLAB仿真实验,详细讨论了四种阈值函数算法.最后,对这几种算法的降噪效果进行了比较.     

基于CUDA架构与B样条的实时锥束CT重建算法

随着X线探测板数据采集速度的快速发展,研究者开始利用C臂机采集投影数据并重建断层图像,用于手术导航或者放射治疗.但是普通PC的重建速度慢,很难匹配硬件数据采集速度,限制了其在实时临床环境中的应用.本文提出一种基于CUDA(Compute Unified Device Architecture)架构的改进FDK算法,利用GPU(Graphic Porcessing Unit)显卡的并行计算能力实现了实时CT重建,并通过B样条插值提高重建图像的质量,在实时临床环境中具有很好的应用价值.