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Generalizing wavelets by adding desired redundancy and flexibility, framelets (a.k.a. wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multi-scale...
The Strong Restricted Isometry Property of Sub-Gaussian Matrices and the Erasure Robustness Property of Gaussian Random FramesDownload
In this thesis we will study the robustness property of sub-gaussian random matrices. We first show that the nearly isometry property will still hold with high probability if we erase a certain portion of rows from a sub-gaussian matrix, and we will estimate the erasure ratio with a given small...