Frames in Compressive Sensing and Approximate Signal Recovery Pertaining to Physical Sensing Matrices.

摘要

In a series of papers we made a deep study of phase retrieval which has a broad spectrum of engineering applications and even will be needed to align the mirrors of the new James Webb Space Telescope. In some applications, such as crystal twinning, we have to recover the phase of a signal from its projections onto subspaces of the space. It was believed that projections give much less information than vectors and so it should take many more projections than vectors to do phase retrieval. We proved the surprising result that actually, it takes fewer projections than vectors to do phase retrieval. We introduced two new areas of research: Integer frames and weaving frames, and developed their basic properties. Weaving frames have application for pre-processing signals. Integer frames have the major advantage that they can process signals without the first level of quantization errors since they do not need approximations to their coefficients.