- #1
Squatchmichae
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I am trying to ultimately find the projector onto a convex set defined in a non-explicit way, for a seismic processing application.
The signals in question are members of some Hilbert Space H and the set membership requires that they must correlate with each other above some scalar [itex]\rho[/itex], given that the known signal [itex]\textbf{w}[/itex] is in the set. Symbolically, I want to find a projector [itex]\textit{P}[/itex] onto the convex set [itex]\textit{C}[/itex]:
\begin{equation}
C = \left\{\mathbf{u}(t) : \left\langle \hat{\mathbf{u}}(t),\hat{\mathbf{v}}(t) \right\rangle \geq\rho_{0}, \forall \mathbf{v}(t) \in C, \quad where \quad \mathbf{w}(t) \in C \right\},
\end{equation}
Any intermediate help is appreciated, i.e., is there an equivalent way to formulate this set, that make finding the projector easier?
The signals in question are members of some Hilbert Space H and the set membership requires that they must correlate with each other above some scalar [itex]\rho[/itex], given that the known signal [itex]\textbf{w}[/itex] is in the set. Symbolically, I want to find a projector [itex]\textit{P}[/itex] onto the convex set [itex]\textit{C}[/itex]:
\begin{equation}
C = \left\{\mathbf{u}(t) : \left\langle \hat{\mathbf{u}}(t),\hat{\mathbf{v}}(t) \right\rangle \geq\rho_{0}, \forall \mathbf{v}(t) \in C, \quad where \quad \mathbf{w}(t) \in C \right\},
\end{equation}
Any intermediate help is appreciated, i.e., is there an equivalent way to formulate this set, that make finding the projector easier?
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