快速小波变换与去噪研究

Study on Fast Wavelet Transformation and Noise Elimination

构造紧支集小波正交基时发现：紧支集正交小波基函数与地震波极为相似，比较适合地震资料处理．利用快速小波变换及小波变换的正交分解性将仿真地震记录在时间域分解成不同尺度下的地震记录．原始记录的频谱和重建记录的频谱表明：数字信号按小波变换进行正交分解重建具有很好的保真性．为检验快速小波变换去噪效果，对仿真地震记录加入随机噪音，利用快速小波变换去噪，即求取Ｌ２（Ｒ）空间各正交基的投影，比较去噪前后的仿真地震记录，随机噪音得到压制，且信号不失真．

Through construct tight branch collection of orthogonal wavelet base, we find that tight branch collection of orthogonal base wavelet function resembles real seismic wave. Taking advantage of fast wavelet transform and its orthogonal decompose property we decomposed the simulate seismic record into different scales of seismic records in time zone. Through reconstruct and analysis, the frequency spectrum of the simulate seismic record and that of reconstrcuted record show that digital signal decomposed and reconstructed by wavelet transform has high fidelity. Adding random noise into the simulate seismic record will eliminate noise by fast wavelet transform, that is to calculate the project of every orthogonal wavelet base in L 2(R) . Comparing the record with eliminated noise record, the random noise is depressed and the signal is not distorted.