Efficient seismic imaging with spectral projector and joint sparsity

In this thesis, we investigate the potential of improving the eciency of seismic imaging with two advanced techniques: the spectral projector and the 'joint sparsity'. The spectral projector offers an eigenvalue decomposition free computation routine that can filter out unstable evanescent wave com- ponents during wave equation based depth extrapolation. 'Joint sparsity' aims to improve on the pure sparsity promoting recovery by making use of additional structure information of the signal. Besides, a new sparsity optimization algorithm - PQNL1 - is proposed to improve both theoretical convergence rate and practical performance for extremely large seismic imaging problems.