the Restricted Isometry Property of an observation matrix in the CS framework is given below.
According to my experience, the difficulty is how to realize the multiplication of the two variables,i.e. 
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This problem is non-convex. Even if you gridded \delta, treating \delta as input data, for each value of \delta in the grid, the constraints would still be non-convex due to having norms on the wrong sides of inequality constraints.