Target imaging under robust sparsity recovery

Creating a dictionary is essential in utilizing compressed sensing concept to explore sparsity for many applications. On one hand, a large and fine dictionary is needed to achieve high estimation accuracy. On the other hand, big dictionary also introduce heavy computations. Furthermore, one can imagine that no matter how fine we grid the domain to create the dictionary, there always will be off-grid problem, namely, the parameters we try to estimate do not lie on the grids. In this work, we model this off-grid problem as a basis mismatch. To tackle this issue, we propose to utilize the robust optimization techniques such as stochastic robust and worst case optimization. Simulations in imaging applications confirm that proposed robust compressed sensing approaches indeed outperform the traditional one.