1 Introduction
Wavelet transforms have been successfully used in many scientific fields such as image compression, image denoising, signal processing, computer graphics,and pattern recognition, to name only a few.Donoho and his coworkers pioneered a wavelet denoising scheme by using soft thresholding and hard thresholding. This approach appears to be a good choice for a number of applications. This is because a wavelet transform can compact the energy of the image to only a small number of large coefficients and the majority of the wavelet coeficients are very small so that they can be set to zero. The thresholding of the wavelet coeficients can be done at only the detail wavelet decomposition subbands. We keep a few low frequency wavelet subbands untouched so that they are not thresholded. It is well known that Donoho's method offers the advantages of smoothness and adaptation. However, as Coifman
1.介紹
小波變換已成功地應(yīng)用于許多科學(xué)領(lǐng)域，如圖像壓縮，圖像去噪，信號(hào)處理，計(jì)算機(jī)圖形，IC和模式識(shí)別，僅舉幾例。Donoho和他的同事們提出了小波閾值去噪通過(guò)軟閾值和閾值.這種方法的出現(xiàn)對(duì)于大量的應(yīng)用程序是一個(gè)好的選擇。這是因?yàn)橐粋€(gè)小波變換能結(jié)合的能量,在一小部分的大型系數(shù)和大多數(shù)的小波系數(shù)中非常小,這樣他們可以設(shè)置為零。這個(gè)閾值的小波系數(shù)是可以做到的只有細(xì)節(jié)的小波分解子帶。我們有一些低頻波子帶不能碰觸，讓他們不閾值。眾所周知，Donoho提出的方法的優(yōu)勢(shì)是光滑和自適應(yīng)。然而，Coifman和Donoho指出，這種算法展示出一個(gè)視覺(jué)產(chǎn)出：吉布斯現(xiàn)象在鄰近的間斷。因此，他們提出對(duì)這些產(chǎn)出去噪通過(guò)平均抑制所有循環(huán)信號(hào)。實(shí)驗(yàn)結(jié)果證實(shí)單目標(biāo)識(shí)別小波消噪優(yōu)于沒(méi)有目標(biāo)識(shí)別的情況。Bui和Chen擴(kuò)展了這個(gè)目標(biāo)識(shí)別計(jì)劃，他們發(fā)現(xiàn)多小波的目標(biāo)識(shí)別去噪的結(jié)果比單小波去噪的結(jié)果要好。蔡和西爾弗曼提出了一種閾值方案通過(guò)采取相鄰的系數(shù)。他們結(jié)果表現(xiàn)出的優(yōu)勢(shì)超于了傳統(tǒng)的一對(duì)一小波消燥。Chen和Bui擴(kuò)展這個(gè)相鄰小波閾值為多小波方法。他們聲稱(chēng)對(duì)于某些標(biāo)準(zhǔn)測(cè)試信號(hào)和真實(shí)圖像相鄰的多小波降噪優(yōu)于相鄰的單一小波去噪。陳等人提出一種圖像去噪是考慮方形相鄰的小波域。陳等人也嘗試對(duì)圖像去噪自定義小波域和閾值。實(shí)驗(yàn)結(jié)果表明：這兩種方法產(chǎn)生更好的去噪效果。