Computational time-reversal imaging with a small number of random and noisy measurements

Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator, obtained through the singular value decomposition of the frequency response matrix. Here, we discuss the image recovery problem from a small number of random and noisy measurements, and we show that this problem is equivalent to a randomized approximation of the null subspace of the frequency response matrix. PACS: 02.30.Zz Inverse problems 43.60.Pt Signal processing techniques for acoustic inverse problems 43.60.Tj Wave front reconstruction, acoustic time-reversal