Target-oriented imaging of acoustic media using unknown and uncontrolled random sources

Abstract

Target-oriented imaging seeks to localize inhomogeneities within a medium from measurements of the waves that scatter off them. Conventionally, this requires both knowledge and control of the sources used to illuminate the scattering targets. In this thesis, I explore and develop methods for imaging arbitrarily complex acoustic scatterers that require neither knowledge nor control of the sources of illumination. Inspired by random-illumination imaging experiments in optics, I first provide a geometrical explanation of the memory effect, a phenomenon in which the interference of scattered waves from a random medium preserves information carried by the wave incident to the medium. I simulate the time dependence of the memory effect using short-duration impulses that transmit through a collection of random point scatterers. Next, I demonstrate the ability to image strongly scattering targets in the presence of unknown and uncontrolled random sources. The linear sampling method is used to invert the total recorded waveforms and obtain an image of the targets. Successful imaging under such conditions requires the persistent radiation of scattered energy that can be amplified and detected in the recorded data. Subsequently, I introduce an imaging method based on inverting the Lippmann-Schwinger equation of acoustic scattering theory. I compare the proposed Lippmann-Schwinger inversion with the linear sampling method and explore their physical bases. Numerical experiments are performed to quantitatively assess the two methods. Finally, I resolve the dependence of the linear sampling method on an ambiguous time parameter and establish a physical framework for the method's interpretation. Numerical algorithms are given to properly and efficiently implement the method in both the time and frequency domains. I validate the algorithms and interpretation of the method with numerical examples.