同質成核英語怎麼說及英文翻譯

『壹』 手工英語翻譯~

這篇更專業了，我盡力翻譯了，希望對你有點幫助。
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To overcome this problem, the Wiener filter has been extended to multiple-bases representations for noise removal. Mihcak and Kozintsev^([1]) approached the signal estimation problem from the perspective of designing the Wiener filter in the wavelet domain. The technology indirectly yields an estimate of the signal subspace that is leveraged into the design of the filter. This paper studies the problem of nonlinear Wiener filtering in reprocing kernel Hilbert spaces via least square support vector regression, The method reflected new perspectives within the framework of kernel methods for denoising problem. Experimental results confirm a significant improvement in image denoising.

Least support squares vector regression is a new universal learning machine proposed by Suykens etal.^([2]) Let x∈R^d, y∈R, R^d represent input space, d is the dimension. By some nonlinear mapping ∅, x is mapping into some a prior chosen Hilbert space spanned by the linear combination of a set of functions.
with ∅(x): R^d→R.
Such that the following regularized risk function J is minimized:
The parameter γ is a positive regularization constant. After elimination of w,e one obtains the solution:
Where Y=[y_1…y_N], ρ_1=[1…1], α=[α_1…α_N] and Ω=K+γ^(-1)I . The resulting least support squares vector regression model for function estimation becomes:
where K(x,x_i)=∅(x) ∅(x_i)(i=1,…,N) is the kernel function and must satisfy the Mercer condition,^([3]) α are Lagrange multipliers and b almost equals the mean of y.

Consider a 2D image consisting of a matrix of M=N×N pixels, the observation image can be regarded as a function in pixel areas y=f(i.j); R^2→R^1, where input (i,j) is 2D vector equals to the row and column indices of that pixel, where output y is the approximated intensity value.^([4]) The Lagrange multipliers α_(i,j) of the observed image pixel y(i,j) can be easily calculated using Eq.(3).
where A=Ω^(-1), B=(I^T Ω^(-1))/(I^T Ω^(-1) I) and O_α is a N×N matrix defined by A(I-IB). Notice that, the Lagrange multipliers α_(i,j) of the observed image pixel y(i,j) is determined by the multiplication of the matrix O_α and the observed image Y. That is, the Lagrange multipliers are influenced by the clean image S and random noise N. As in Eq.(4), the observed image can be reconstructed by a linear combination of kernels with weights equal to the values of Lagrange multipliers and an appropriate support vector regression can concentrate the signal energy into a number of support vectors(SVs) that α_(i,j) is nonzero.

The localization of SVs is particularly appropriate for imaging applications, where it is crucial to preserve fine details like edges and textures. Pixels with positive Lagrange values try to raise the grey levels of themselves and their neighbors, while those with negative Lagrange multipliers will try to rece the grey levels and they appear darker.

Therefore, the Lagrange multipliers effectively weigh the kernel functions to estimate intensity value of image. Furthermore, random noise can be considered as forces that try to make Lagrange multipliers to oscillate above and below the standard value. The noise can be reced by smoothing the value of Lagrange multipliers, whereas sharp edges may be preserved within certain ranges which rely on a suitable kernel function possessing the capability of nonlinear representation.
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翻譯如下
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為了解決這個問題，我們把維納濾波法擴展到多基表述來除噪音。Mihcak和Kozintsev^([1]) ，從在小波域里設計維納濾波器的角度來解決信號估算問題。這種技術間接地給出了一個可以補充到濾波器的設計中的信號子空間的估值。這篇論文研究非線性維納濾波法通過最小二乘支持向量回歸在再生成核希爾伯特空間中的問題，以及在降噪問題核心演算法的構架內新角度下的方法。實驗的結果確認了圖像降噪中的顯著優化。

最小二乘向量回歸是一種由Suykens etal.^([2])提出的新的通用學習機器。讓x∈R^d, y∈R, R^d代表輸入空間，d代表維度。通過一些非線性映射∅ ，x會映射到一些事先選好的由一組函數的線性組合擴展開來的希爾伯特空間。
由∅(x): R^d→R.
於是下面的調整風險函數被最小化：
系數γ是正的調整常數。消去w，e後，解得：
這里Y=[y_1…y_N], ρ_1=[1…1], α=[α_1…α_N] ,Ω=K+γ^(-1)I
得出的用來函數估值的最小二乘向量回歸模型變成了：
這里K(x,x_i)=∅(x) ∅(x_i)(i=1,…,N)成為核函數，而且必須符合Mercer條件^([3])， α是拉格朗日乘數同時b近乎等於y的平均值。

考慮一張由一個N×N像素的矩陣M組成的二維圖像，這張觀測用的圖像可以視作一個像素麵積y=f(i.j); R^2→R^1的函數，這里的輸入(i,j)是等於那個像素排和列的針數的二維向量，輸出y是近似的發光量值。^([4]) 觀測圖像像素y(i,j)的拉格朗日乘數α_(i,j)可以用等式(3)輕松計算得到。
這里A=Ω^(-1), B=(I^T Ω^(-1))/(I^T Ω^(-1) I) ，而 O_α即是用A(I-IB)定義的N×N矩陣。
注意到，
觀測圖像像素y(i,j)的拉格朗日乘數α_(i,j)是由矩陣O_α和觀測像Y的乘積決定的。也就是說，拉格朗日乘數是會被清晰圖像S和隨機噪音N共同影響。如等式4所示，觀測像可以通過權值等於這些拉格朗日乘數值的核函數的線性組合來重建，同時一個合適的支持向量回歸可以把信號能量集中到一些α_(i,j)為非零值的支持向量中去（SVs）。

支持向量本地化對成像應用特別合適，這對保護圖像邊緣和圖像紋理十分重要。有正的拉格朗日乘數值的像素試著去提升自己和自己周圍的灰階，而同時有負的拉格朗日乘數的像素會試著減少灰階，他們看起來會更暗。

因此，拉格朗日乘數能有效地給核函數加權來估算圖像亮度值。另外，隨機噪音能夠被視作是試著使拉格朗日乘數在其標准值上下震盪的外力。噪音可以通過平滑化拉格朗日乘數來減少，然而銳邊可能要靠一個合適的有非線性表述能力的核函數在一定的范圍內進行保邊。
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