Hybrid Fourier-wavelet Image Denoising And Signal Processing Of Laser Screen Target System

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.