英语翻译Note that also this basis is orthonormal since [G(−1)][G(−1)]t=I4.We have now decomposedour original signal x into an orthogonal direct sum x = x(−1)+y(−1) where x(−1) is theprojection of x onto V−1 as

英语翻译Note that also this basis is orthonormal since [G(−1)][G(−1)]t=I4.We have now decomposedour original signal x into an orthogonal direct sum x = x(−1)+y(−1) where x(−1) is theprojection of x onto V−1 as
英语翻译
Note that also this basis is orthonormal since [G(−1)][G(−1)]t=I4.We have now decomposed
our original signal x into an orthogonal direct sum x = x(−1)+y(−1) where x(−1) is the
projection of x onto V−1 as given above and y(−1) is the projection of x onto W−1.This
projection is given by y(−1)= [G(−1)]tY(−1) with Y(−1)=G(−1)X.This is depicted in Figure
1.4.The sum of the pictures 1.3 and 1.4 would give the Figure 1.2 back (up to a scaling
Figure 1.4:Projection on orthogonal complement and 1 basis function
〓
factor).
y(−1)
ψ−1,3
Mathematically,we have represented the original signal with repect to a new basis,
namely the columns of the matrix E(−1)=I8[T(−1)]t where (T(−1))t = [(H(−1))t(G(−1))t]
describes the basis transformation.The new coordinates for this basis are given by
X(−1)
Y(−1)=
H(−1)
G(−1)X= T(−1)X.
Now suppose that the low resolution picture of Figure 1.3 is still too high for the screen
we have available,then we can repeat the same kind of operation to this picture.Thus,we

英语翻译Note that also this basis is orthonormal since [G(−1)][G(−1)]t=I4.We have now decomposedour original signal x into an orthogonal direct sum x = x(−1)+y(−1) where x(−1) is theprojection of x onto V−1 as
请注意,同时在此基础上,是正交自[克（ -1 ） ] [克（ -1 ） ]吨= i4 .我们现在已经开始腐烂
我们原来的信号x成为一个正交直x = x （下-1 ） + Y （下-1 ） ,其中X （ -1 ）是
投影的X上的V - 1鉴于以上和Y （ -1 ）是投影的X上的W - 1 .这个
预测是鉴于由Y （ -1 ） = [克（ -1 ） ]性（ -1 ）与Y （ -1 ） =克（ -1 ）十.这是所描绘的数字
1.4 .总和的图片1.3和1.4将给予见图1.2回（截至1缩放
图1.4 ：投影对正交补和1个基础功能
〓
因子） .
Y （下-1 ）
ψ - 1 ,3
在数学方面,我们已为代表的原始信号与repect到一个新的基础上,
即列矩阵（ -1 ） = i8 [吨（ -1 ） ]吨在哪里（吨（ -1 ） ）笔= [ （ H （下-1 ） ）吨（克（ -1 ） ）笔]
描述的基础上转型.新的坐标在此基础上,给出了由
× （ -1 ）
Y （下-1 ） =
的H （ -1 ）
克（ -1 ） × =吨（ -1 ）十.
现在假设分辨率低的图片图1.3是仍然过高,为屏幕
我们有可用的,那么我们可以重复同样的种运作此图片.因此,我们