Multiresolution approximations and wavelet orthonormal bases of ๐ฟยฒ(๐
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Multiresolution approximations and wavelet orthonormal bases of ๐ฟยฒ(๐
)
A multiresolution approximation is a sequence of embedded vector spaces <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis bold upper V Subscript j Baseline right-parenthesis Subscript j element-of z"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">V</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>j</mml:mi> </mml:msub> </mml:mrow> <mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> โฆ