I am trying to ultimately find the projector onto a convex set defined in a non-explicit way, for a seismic processing application.(adsbygoogle = window.adsbygoogle || []).push({});

The signals in question are members of some Hilbert SpaceHand 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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# Convex set for similarity constraint

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