混合傅立叶—小波图像降噪及激光测速靶信号处理
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摘要
在图像的采集和传输过程中,图像经常会被噪声所污染,因此在对图像进行使用或进一步处理前,需要去除图像中的噪声。去除噪声的同时不可避免地会扭曲图像,图像降噪实际上就是要在降低噪声水平和保留图像特征(如图像中的边)之间作权衡。基于傅立叶变换的频域滤波法因为其简单而被经常使用。应用傅立叶变换进行滤波时,我们假设图像的傅立叶变换系数主要集中在低频部分,应用低通滤波器将认为是噪声的高频系数去除或收缩,便可以达到滤波的目的。理论上来讲,用变换域滤波法进行滤波时,若只有少数的图像的变换域系数的幅值较大,而大部分的系数幅值都较小,几乎为零(称之为图像能在变换域中被稀疏表示),则滤波效果会好。但是图像能否在变换域中被稀疏表示和图像的特征、变换的种类有关。由于现实世界的图像千差万别,没有一种变换方法能对所有类型的图像进行稀疏表示。傅立叶变换能有效地稀疏表示图像中有一定变化周期规律的纹理部分和变化平缓的部分,但是不能有效的表示图像中的突变部分,如图像中的边。小波变换能稀疏表示包含尖锐变化部分的信号如图像中的边,但缺点是不能有效表示图像中的纹理和缓慢变化的部分。因此,如果能有一种滤波算法将傅立叶变换和小波变换组合起来,有可能获得比单独使用傅立叶变换或小波变换都要好的滤波效果。本文提出一种混合傅立叶小波图像降噪方法:先在傅立叶域降噪,再在小波域降噪。由于小波变换比傅立叶变换更适合处理图像这样的非平稳信号,因此在傅立叶域中的降噪要保守一些,起的是辅助作用,以免使图像过分扭曲。实验结果表明,这种混合算法能够取得比基于小波变换的图像降噪法好的降噪效果。
激光测速靶是一种区截测速装置,即根据子弹通过两个靶面的时间间隔和两个靶面间的距离计算出子弹的平均速度。对激光测速靶的信号进行分析,准确计算出子弹穿过靶面的时刻对提高测量精度有非常重要的意义。激光测速靶的信号分析是一种信号奇异点位置检测问题。本文提出一种使用连续小波变换分析激光测速靶的信号的方法。该算法从大尺度到小尺度沿着小波变换模极大线确定信号奇异点的位置,从而判断出子弹的过靶时刻。由于在大尺度上噪声的小波变换系数的幅值比信号的小波变换系数的幅值小,该算法能有效抑制噪声的影响。实验结果表明应用小波分析激光靶的信号提高了测量的精度和可靠性。
During image acquisition and transmission, digital images are always contaminated by noise. So it is necessary to remove noise before the images data is used or analyzed. While noise is suppressed, images are also distorted inevitably. In fact, image denoising is a trade-off between noise suppression and the preservation of actual image discontinuities such as edges. Frequency domain image denoising methods are popularly used because of simplicity. Frequency domain filtering assume that Fourier coefficients of original image are mainly concentrated in lower frequency so noise is suppressed by remove the higher frequency coefficients using a lowpass filter. Theoretically, if only few coefficients of images are high-magnitude and most coefficients are close to zero (the image is sparsely represented in the transform domain), the performance of transform domain denoising methods would be better. But the sparsity of representation depends on both the transform and the original image’s property. The great varieties in natural images makes impossible for any fixed transform to achieve good sparsity for all class of images. For example, Fourier transform is effective in representing textures and smooth transitions of an image but would perform poorly for singularities such as image edges. The strength of the wavelet domain is that it sparsely represents classes of signals containing singularities and sharp transitions. However, the weakness of the wavelet domain is that it is not effective in representing textures and smooth transitions. So a denoising algorithm combining Fourier transform and wavelet transform can increase the filtering performance. In this paper, a hybrid Fourier-wavelet denoising method is introduced. The main steps of the proposed method are as follows. The noisy image is denoised in Fourier domain firstly so that the noise level is lowered. Then secondly the remaining noise is removed in wavelet domain. Because wavelet transform is more suitable for image representation than Fourier transform, denoising in Fourier transform should be conservative so that the original image is not distorted greatly. Experiments demonstrate that our proposed method is superior to the recently developed image denoising methods based on wavelet transform.
Laser screen target is a velocity measurement system for projected bullet. The average velocity is worked out based on the time during which the bullet passes through two screen targets and the distance between the two screen targets. It is important to estimate the time at which the bullet passes through the target by analyzing the signal of the target system. The signal analysis of laser screen target system is a problem of localization of singular point. An algorithm for processing the signal of the target system using wavelet is introduced. Searching along wavelet transform maxima lines from large scale to small scale the singularity point of the signal is discriminated. So the time at which the bullet passes through the target is obtained. Because the amplitude of wavelet coefficients of noise is smaller than that of signal, the influence of noise can be decreased. Experimental results show that the proposed algorithm makes measurement more precise and reliable.
激光测速靶是一种区截测速装置,即根据子弹通过两个靶面的时间间隔和两个靶面间的距离计算出子弹的平均速度。对激光测速靶的信号进行分析,准确计算出子弹穿过靶面的时刻对提高测量精度有非常重要的意义。激光测速靶的信号分析是一种信号奇异点位置检测问题。本文提出一种使用连续小波变换分析激光测速靶的信号的方法。该算法从大尺度到小尺度沿着小波变换模极大线确定信号奇异点的位置,从而判断出子弹的过靶时刻。由于在大尺度上噪声的小波变换系数的幅值比信号的小波变换系数的幅值小,该算法能有效抑制噪声的影响。实验结果表明应用小波分析激光靶的信号提高了测量的精度和可靠性。
During image acquisition and transmission, digital images are always contaminated by noise. So it is necessary to remove noise before the images data is used or analyzed. While noise is suppressed, images are also distorted inevitably. In fact, image denoising is a trade-off between noise suppression and the preservation of actual image discontinuities such as edges. Frequency domain image denoising methods are popularly used because of simplicity. Frequency domain filtering assume that Fourier coefficients of original image are mainly concentrated in lower frequency so noise is suppressed by remove the higher frequency coefficients using a lowpass filter. Theoretically, if only few coefficients of images are high-magnitude and most coefficients are close to zero (the image is sparsely represented in the transform domain), the performance of transform domain denoising methods would be better. But the sparsity of representation depends on both the transform and the original image’s property. The great varieties in natural images makes impossible for any fixed transform to achieve good sparsity for all class of images. For example, Fourier transform is effective in representing textures and smooth transitions of an image but would perform poorly for singularities such as image edges. The strength of the wavelet domain is that it sparsely represents classes of signals containing singularities and sharp transitions. However, the weakness of the wavelet domain is that it is not effective in representing textures and smooth transitions. So a denoising algorithm combining Fourier transform and wavelet transform can increase the filtering performance. In this paper, a hybrid Fourier-wavelet denoising method is introduced. The main steps of the proposed method are as follows. The noisy image is denoised in Fourier domain firstly so that the noise level is lowered. Then secondly the remaining noise is removed in wavelet domain. Because wavelet transform is more suitable for image representation than Fourier transform, denoising in Fourier transform should be conservative so that the original image is not distorted greatly. Experiments demonstrate that our proposed method is superior to the recently developed image denoising methods based on wavelet transform.
Laser screen target is a velocity measurement system for projected bullet. The average velocity is worked out based on the time during which the bullet passes through two screen targets and the distance between the two screen targets. It is important to estimate the time at which the bullet passes through the target by analyzing the signal of the target system. The signal analysis of laser screen target system is a problem of localization of singular point. An algorithm for processing the signal of the target system using wavelet is introduced. Searching along wavelet transform maxima lines from large scale to small scale the singularity point of the signal is discriminated. So the time at which the bullet passes through the target is obtained. Because the amplitude of wavelet coefficients of noise is smaller than that of signal, the influence of noise can be decreased. Experimental results show that the proposed algorithm makes measurement more precise and reliable.
引文
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