Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The ๐ฟ^{๐}-theory
Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The ๐ฟ^{๐}-theory
We prove that the exact reconstruction of a function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="s"> <mml:semantics> <mml:mi>s</mml:mi> <mml:annotation encoding="application/x-tex">s</mml:annotation> </mml:semantics> </mml:math> </inline-formula> from its samples <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="s left-parenthesis x Subscript i Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">s (x_i)</mml:annotation> โฆ