The research of solve measurement dimension for inverse problem based on convex optimization

This paper studies how to transform vector to be estimated recovery problem into a convex optimization problem based on measure values. Restore ratio of vector to be estimated depends on the measured values dimension. So we can transform the problem of measurement dimension into the problem of calculating the tangent cone Gaussian width that induced by atomic norm. And the problem of solve Gaussian width mainly use dual structure. Eventually solving the dimension of the measurement depends on solving the problem of dual cone Gaussian width. Finally, this paper solves the sparse vector and the low-rank matrix through computer simulation software. Verify the validity of the number of dimensions of the measurements that determined.