【正文】 所使用的小波。小波分析和 STFT的分析方法類似，在這個意義上說，就是信號和一個函數(shù)相乘， {它的小波 }，類似的 STFT的窗口功能，并轉換為不同分段的時域信號。psi(t)為轉化功能，它被稱為母小波。這個詞意味著母波在支持不同類型波的轉型過程中起主要作用，或者叫母小波。但是，我們沒有一個頻率參數(shù)，因為我們之前 STFT。 雖然時間和頻率分辨率的問題是一種物理現(xiàn)象（海森堡測不準原理）無論是否使用變換，它都存在，但是它可以使用替代方法分析，稱為信號多分辨率分析（ MRA）。這種方法是十分有意義的，特別是當手頭的信號高頻成分持續(xù)時間短和低頻成分持續(xù)時間長時。 外文文獻譯文 3 在特定的信號分析中任何性能的變化都是高度基于基礎功能的變換。計算結果表明，優(yōu)化的混合小波包基可更好的進行數(shù)字信號壓縮，同時提供開發(fā)選取這些最優(yōu)基的方法， 離散小波變換（小波變換）的特點可以看做一對遞歸應用的高通和低通濾波器形成了一個鏡像濾波器。 計算小波包分解。小波包計算特點是靠二叉樹的每個分支代表高通和低通濾波器的輸出濾波根節(jié)點形成十進制圖示完成計算的。由于實驗研究者對給定小波選擇問題有一些經驗，所以他們對于開發(fā)選擇可靠適合的特定信號表示基的方法可參考曾經的試驗經驗。 選擇適當?shù)恼荤R像濾波器實質上影響壓縮方案的性能，對于不同的正交鏡像濾波器最好最簡單的解決 方案是選擇最好中的最好的。這是因為一個小波變換能結合的能量 ,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 ,這樣他們可以設置為零。然而， Coifman和 Donoho指出，這種算法展示出一個視覺產出：吉布斯現(xiàn)象在鄰近的間斷。蔡和西爾弗曼提出了一種閾值方案通過采取相 鄰的系數(shù)。陳等人提出一種圖像去噪是考慮方形相鄰的小波域。將小波變換產生的二維圖像在每個規(guī)模大的小波系數(shù)的分解。沿著“ x1cos_ + x2sin_ = 常數(shù)” 一條線的脊波是不變的。這種近似二元樹性能的復雜變性小波和良好性能的脊波使我們有更好的方法去圖像去噪。實驗結果在第 。在另一方面 ,利用小波變換產生的多大的小波系數(shù)對每個尺度邊緣二維小波分解。 。輸入信號的一個小小的改變能夠引起輸出小波系數(shù)很大的變化。用這種方法我們可以優(yōu)秀品質的脊波變換用來替換二元樹發(fā)雜脊波。為了得到降噪的復雜脊波系數(shù)我們通常在當前象素地位 對降噪的復雜脊波系數(shù)進行平均 4 份。我們使用下列硬閾值規(guī)則估算未知的脊波系數(shù)。當這個噪音系數(shù)大于 30 時，我們用k=6首次分解尺度和 k=5分解其他尺度。 我們稱這種算法叫，同時我們使用普通的脊波。該算法的其他計算步驟保持相同。這表明 ComRidgeletSrink 對于自然圖像去噪是一個很好的選擇。 VisuShrink 是通用軟閾值去噪技術。峰值信噪比的實驗結果顯示的表 32*32或者 64*64是最好的選擇。j (B(i。在這樣的情況下， VisuShrink 將產生比原來的去噪圖像更糟的結果。 ComRidgeletShrink 超越VisuShrink的表現(xiàn)更重要的是所有噪音水平和圖像測試。實驗結果表明，利用小波去噪能實現(xiàn)對各種信號的去噪，且效果比較明顯。s method offers the advantages of smoothness and adaptation. However, as Coifman and Donoho pointed out, this algorithm exhibits visual artifacts: Gibbs phenomena in the neighbourhood of discontinuities. Therefore, they propose in a translation invariant (TI) denoising scheme to suppress such artifacts by averaging over the denoised signals of all circular shifts. The experimental results in confirm that single TI wavelet denoising performs better than the nonTI case. Bui and Chen extended this TI scheme to the multiwavelet case and they found that TI multiwavelet denoising gave better results than TI single wavelet denoising. Cai and Silverman proposed a thresholding scheme by taking the neighbour coeficients into account Their experimental results showed apparent advantages over the traditional termbyterm wavelet and Bui extended this neighbouring wavelet thresholding idea to the multiwavelet case. They claimed that neighbour multiwavelet denoising outperforms neighbour single wavelet denoising for 外文文獻原文 5 some standard test signals and reallife et al. proposed an image denoising scheme by considering a square neighbourhood in the wavelet domain. Chen et al. also tried to customize the wavelet _lter and the threshold for image denoising. Experimental results show that these two methods produce better denoising results. The ridgelet transform was developed over several years to break the limitations of the wavelet transform. The 2D wavelet transform of images produces large wavelet coeficients at every scale of the so many large coe_cients, the denoising of noisy images faces a lot of diffculties. We know that the ridgelet transform has been successfully used to analyze digital images. Unlike wavelet transforms, the ridgelet transform processes data by first puting integrals over different orientations and locations. A ridgelet is constant along the lines x1cos_ + x2sin_ = constant. In the direction orthogonal to these ridges it is a have been successfully applied in image denoising recently. In this paper, we bine the dualtree plex wavelet in the ridgelet transform and apply it to image denoising. The approximate shift invariance property of the dualtree plex wavelet and the good property of the ridgelet make our method a very good method for image results show that by using dualtree plex ridgelets, our algorithms obtain higher Peak Signal to Noise Ratio (PSNR) for all the denoised images with di_erent noise anization of this paper is as follows. In Section 2, we explain how to incorporate the dualtree plex wavelets into the ridgelet transform for image denoising. Experimental results are conducted in Section 3. Finally we give the conclusion and future work to be done in section 4. IMAGE DENOISING BY USING COMPLEX Ridgelets Discrete ridgelet transform provides nearideal sparsity of representation of both smooth objects and of objects with edges. It is a nearoptimal method of denoising for Gaussian noise. The ridgelet transform can press the energy of the image into a smaller number of ridgelet coe_cients. On the other hand, the wavelet transform produces many large wavelet coe_cients on the edges on every scale of the 2D wavelet deposition. This means that many wavelet coe_cients are needed in order to reconstruct the edges in the image. We know that approximate Radon transforms for digital data can be based on discrete fast Fouriertransform. The ordinary ridgelet transform can be achieved as follows: 1. Compute the 2D FFT of the image. 2. Substitute the sampled values of the Fourier transform obtained on the square lattice with sampled values on a polar lattice. 3. Compute the 1D inverse FFT on each angular line. 4. Perform the 1D scalar wavelet transform on the resulting angular lines in order to obtain the ridgelet coe_cients. It is well known that the ordinary discrete wavelet transform is not shift invariant because of the decimation operation during the transform. A small shift in the input signal can cause very di_erent output wavelet coe_cients. In order to overe this problem, Kingsbury introduced a new kind of wavelet transform, called the dualtree plex wavelet transform, that exhibits approximate shift invariant 外文文獻原文 6 property and improved angular resolution. Since the scalar wavelet is not shift invariant, it is better to apply the dualtree plex wavelet in the ridgelet transform so that we can have what we call plex ridgelets. This can be done by replacing the 1D scalar wavelet with the 1D dualt