In this thesis, I adopt ideas of finding the structure from randomness to recover the low-rank representations of the full subsurface extended image volumes which can give us access to any elements and image gathers. I derived the time-domain wave-equation based factorization via randomly probing which helps to remove the computational bottlenecks in both wave-equation solves and the imaging conditions. Also, I designed the framework combined with power iterations to increase the recovered accuracy without increasing the probing size. Furthermore, I adopt the low-rank representations for velocity continuation by mapping technique based on invariance relationship. To arrive high-resolution images in complex geological models, least-squares reverse time migrations were proposed, followed with computationally efficient inversion derived from stochastic optimization. How to perform the inversion without prior knowledge of sources is still an open issue. I propose the on-the-fly source estimation technique via variable projection during the inversion of imaging, by solving the least-squares sub-problems with penalties which help to avoid the overfitting to noise in the data. To extend the application of our inversion framework to marine data with strong surface-related multiples that could contribute to illumination, we inject the areal source into Born model, and the related cross-talk between different orders of reflections can be cleaned up in inversion. However, since we use Born modeling only with respect to velocity in the inversion, there will be strong artificial velocity perturbations converted from the strong density variations at the ocean bottom. Without developing the Born modeling with respect to density perturbation, I propose to use a low-rank filter to match the data that containing density-related components to the ideal data that containing velocity-related components, furthermore to remove the artifacts at the ocean bottom. I demonstrate the proposed methods above on 2D experiments and conclude the thesis with an outlook for the current limitations and future research directions.