Wavelet methods for inverting the Radon transform with noisy data

Because the Radon transform is a smoothing transform, any noise in the Radon data becomes magnified when the inverse Radon transform is applied. Among the methods used to deal with this problem is the wavelet-vaguelette decomposition (WVD) coupled with wavelet shrinkage, as introduced by Donoho (1995). We extend several results of Donoho and others here. First, we introduce a new sufficient condition on wavelets to generate a WVD. For a general homogeneous operator, whose class includes the Radon transform, we show that a variant of Donoho's method for solving inverse problems can be derived as the exact minimizer of a variational problem that uses a Besov norm as the smoothing functional. We give a new proof of the rate of convergence of wavelet shrinkage that allows us to estimate rather sharply the best shrinkage parameter needed to recover an image from noise-corrupted data. We conduct tomographic reconstruction computations that support the hypothesis that near-optimal shrinkage parameters can be derived if one can estimate only two Besov-space parameters about an image f. Both theoretical and experimental results indicate that our choice of shrinkage parameters yields uniformly better results than Kolaczyk's (1996) variant of Donoho's method and the classical filtered backprojection method.     

智能靶标目标检测方法研究

在激光模拟训练中,具有智能打击功能的靶标装置可以更加逼真地模拟实战对抗过程,满足智能化军事训练需求。但目前大多数靶标不具备智能打击或反击功能,靶标仅能实现作为目标的被打击功能或者非智能的触发反击功能,模拟训练形式单一,靶标运动或打击功能呈现规律性,不能真实模拟敌方目标主动攻击的能力,因此为适应模拟训练发展的需求实现模拟训练智能化、提高模拟仿真程度就需要通过智能靶标来模拟敌方目标进行作战。在智能靶标的研制过程中其中首先要解决的问题就是目标检测。本研究最终目标是对战场环境中的单兵目标进行检测并做出攻击活动,故对单兵目标的检测速度和精度有较大要求,本文提出一种基于Yolov5神经网络架构提高目标检测精度、加快目标检测速度的算法,采用改进网络结构对传统的目标检测算法进行优化,保证在输入可见光图像下,能够实现快速检测,并保证检测的精度。     

Wavelet transform based novel edge detection algorithms for wideband spectrum sensing in CRNs

The primary task in cognitive radio is to dynamically explore the radio spectrum and reliably detect the co-existing licensed primary transmissions across a wide-band spectrum. This paper focuses on wavelet transform (WT) based wide-band sensing techniques, which identify the edges of the multiple frequency bands simultaneously. Novel edge detection algorithms are proposed based on continuous WT (CWT) and discrete WT (DWT) techniques, applied on wide-band power spectrum. In CWT based spectrum sensing, logarithmic scaling preceded by a thresholding is performed on the CWT coefficients to enhance the small modulus maxima values at the edges, resulting in better detection probability. Since the logarithmic scaling magnifies the spurious edges, the proposed algorithm increases the false alarm probability at high noise variance. To alleviate this problem, DWT based algorithms are proposed, where DWT performs simultaneous denoising and edge detection. To achieve good detection performance at poor SNR scenario, a moving average filtering strategy is adopted at different levels of DWT based algorithms and better performance is achieved even with lower scale value of DWT, thereby reducing the computation time. Comparative studies show that the proposed algorithms outperform the existing WT based edge detection algorithms in the dynamic and frequency selective channels as well.     

Wavelet methods for spike detection in mouse renal sympathetic nerve activity

Abnormal autonomic nerve traffic has been associated with a number of peripheral neuropathies and cardiovascular disorders prompting the development of genetically altered mice to study the genetic and molecular components of these diseases. Autonomic function in mice can be assessed by directly recording sympathetic nerve activity. However, murine sympathetic spikes are typically detected using a manually adjusted voltage threshold and no unsupervised detection methods have been developed for the mouse. Therefore, we tested the performance of several unsupervised spike detection algorithms on simulated murine renal sympathetic nerve recordings, including an automated amplitude discriminator and wavelet-based detection methods which used both the discrete wavelet transform (DWT) and the stationary wavelet transform (SWT) and several wavelet threshold rules. The parameters of the wavelet methods were optimized by comparing basal sympathetic activity to postmortem recordings and recordings made during pharmacological suppression and enhancement of sympathetic activity. In general, SWT methods were found to outperform amplitude discriminators and DWT methods with similar wavelet coefficient thresholding algorithms when presented with simulations with varied mean spike rates and signal-to-noise ratios. A SWT method which estimates the noise level using a "noise-only" wavelet scale and then selectively thresholds scales containing the physiologically important signal information was found to have the most robust spike detection. The proposed noise-level estimation method was also successfully validated during pharmacological interventions.     

红外目标的边界检测和标注

边界检测和标注是红外目标探测和识别的一个重要环节。自然背景复杂的纹理特征和红外图像中的噪声影响,以及红外目标模糊的边缘,给红外目标的边界检测和分割带来一定的困难。分水岭算法作为一种数学形态学的图像分割方法,为进行目标特征分析和识别提供了可能,然而,分水岭算法产生的过度分割,又为背景和噪声抑制增加了难度。文中在分水岭算法的基础上,结合模糊逻辑方法,对自然背景下的红外人工目标的边界检测和分割以及红外背景的抑制进行了探讨。     

小波包变换及其在电力系统谐波电流检测中的应用

在此阐述了小波变换及小波包变换的基本原理。小波包变换是建立在小波变换的基础上,可以实现对信号的均匀划分,能够更好地提取信号的时频特性。仿真结果表明,小波包变换方法能够正确地提取电力系统的谐波信号,将电流信号中的基波分量和高次谐波分量分离,验证了该方法的有效性。     

小波包分析在薄板腐蚀检测中的应用

本文为了快速检测薄板的腐蚀状况对薄板进行主动的全波检测,首先用压电元件产生激励信号并采集传播后的响应信号,然后利用小波包的高时频分析能力对包含缺陷信息的响应信号进行频率带的细分,对各系数进行重构,提取各频率带信号的能量特征,最后分析缺陷和能量向量的映射关系,并建立能量向量-缺陷映射库,从而可以从能量向量直接判断薄板的健康状况,这为快速检测薄板的腐蚀状况提供一种新的技术手段。用小波包对信号进行处理,可以把信号分解到想要的任意细节,很巧妙地将各个频段信号分离,从而方便的达到提取能量向量的目的。     

Wavelet transform threshold noise reduction methods in the oil pipeline leakage monitoring and positioning system

This letter investigates the wavelet transform, as well as the principle and the method of the noise reduction based on wavelet transform, it chooses the threshold noise reduction, and discusses in detail the principles, features and design steps of the threshold method. Rigrsure, heursure, sqtwolog and minimization four kinds of threshold selection method are compared qualitatively, and quantitatively. The wavelet analysis toolbox of MATLAB helps to realize the computer simulation of the signal noise reduction. The graphics and calculated standard deviation of the various threshold noise reductions show that, when dealing with the actual pressure signal of the oil pipeline leakage, sqtwolog threshold selection method can effectively remove the noise. Aiming to the pressure signal of the oil pipeline leakage, the best choice is the wavelet threshold noise reduction with sqtwolog threshold. The leakage point is close to the actual position, with the relative error of less than 1%.     

基于小波变换的指纹全局方向场重建简

从大型指纹库识别不完整或局部指纹仍然是今天的一大挑战。在此文中,我们研究利用小波变换用于指纹方向场重建问题。特别的,我们提出了一种基于小波的多尺度方法从局部的指纹重建全局拓扑表达。然后提出基于结合参数模型和非参数模型来描述重建问题,我们提供了一般表达式可用于所有有效的反变换模型的解决方案。这种方案允许我们分割保护存在的方向场同时预测丢失的未知部分的结构。我们还开发了基于脊线拓扑特征的一些先验信息来估计丢失的方向结构的算法。我们的统计实验表明我们提出的基于模型的算法能有效的恢复指纹的方向场并应用于指纹匹配,这样重大的提高了局部指纹识别其他模块性能。     

Binary partition trees for object detection

This paper discusses the use of Binary Partition Trees (BPTs) for object detection. BPTs are hierarchical region-based representations of images. They define a reduced set of regions that covers the image support and that spans various levels of resolution. They are attractive for object detection as they tremendously reduce the search space. In this paper, several issues related to the use of BPT for object detection are studied. Concerning the tree construction, we analyze the compromise between computational complexity reduction and accuracy. This will lead us to define two parts in the BPT: one providing accuracy and one representing the search space for the object detection task. Then we analyze and objectively compare various similarity measures for the tree construction. We conclude that different similarity criteria should be used for the part providing accuracy in the BPT and for the part defining the search space and specific criteria are proposed for each case. Then we discuss the object detection strategy based on BPT. The notion of node extension is proposed and discussed. Finally, several object detection examples illustrating the generality of the approach and its efficiency are reported.     

Quadratic Gabor filters for object detection

We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem.     

三维物体表面的小波平滑方法

用结构光方法获取物体表面的三维信息,由于其计算简单,易于实现,在计算机视觉领域获得了广泛的应用。然而由于物体表面反射特性的不均匀性、转台的机械扰动以及初始量化误差,实际得到的物体表面将存在一些形变,影响物体表面特性的计算,文中介绍用结构光获取的三维物体表面的小波平滑方法。首次,将物体表面轮廓线（激光扫描线和截面线）以弧长为参数沿Ｘ、Ｙ、Ｚ三个方向分解,并分别用小波进行平滑处理,然后再将这些平滑后的     

Wavelet packet transform initialization for piecewise polynomialand bandlimited inputs

This paper considers the problem of initializing the wavelet packet transform when the analog input x(t) is either bandlimited or else is piecewise polynomial on the dyadic intervals. This is accomplished by the construction of certain prefilter sequences that are applied to the samples {x_k|x_k=x(kT)} (T is the sampling period). In the piecewise polynomial case, the prefilter sequences are computed with the aid of the interpolatory graphical display algorithm (IGDA), which is used to compute the so-called incremental moment functions of the scaling function φ(t) on the dyadic points. The moments of φ(t) are also employed     

Wavelet transform in scattering data interpolation

A fast algorithm for scattering data interpolation is presented. Based on the multiresolution wavelet transform, a preconditioning scheme is proposed to expedite the slow computation speed in the interpolation problem. By applying the wavelet transform before and after any conventional iterative solving method, fast data interpolation can be easily achieved.<>     

Wavelet localization of the Radon transform

The authors develop an algorithm which significantly reduces radiation exposure in X-ray tomography, when a local region of the body is to be imaged. The algorithm uses the properties of wavelets to essentially localize the Radon transform. This algorithm differs from previous algorithms for doing local tomography because it recovers an approximation to the original image, not the image module the nullspace of the local tomography operator, or the Lambda transform of the image. This is possible because the authors do not truly invert the interior Radon transform, but rather sample the Radon transform sparsely away from the local region of interest. Much attention in the field has been directed towards localized tomography. The authors believe that this technique represents a significant contribution towards this effort     

Algorithms for adaptive transform edge detection

Edge detection in grayscale digital images based on the locations of zero crossings has been investigated. Samples of the image are transformed using the discrete symmetric cosine transform (DSCT) and filtered using truncated time or frequency sampled forms of the Laplacian-of-Gaussian (LOG) filter. This article presents and evaluates adaptive block-based filtering procedures to localize edges based on discrete circular and real transforms. Measures of the signal-to-noise ratio (SNR) and edge localization are provided     

增光子相干态的小波变换

通过量子力学变换理论,结合有序算符内的积分技术,用于信号分析的小波变换可推广到增光子相干态的非经典量子特性研究中.结果表明,增光子相干态的小波变换谱除具有一般小波变换的特性外, 而且随着增光子数的逐渐增大,其对称性被破坏,不断有新的波峰出现.