Generating Pictures from Waves: Aspects of Image Formation

Abstract

The research communities, technologies, and tools for image formation are diverse. On the one hand, computer vision and graphics researchers analyze incoherent light using coarse geometric approximations from optics. On the other hand, array signal processing and acoustics researchers analyze coherent sound waves using stochastic estimation theory and diffraction formulas from physics. The ability to inexpensively fabricate analog circuitry and digital logic for millimeter-wave radar and ultrasound creates opportunities in comparing diverse perspectives on image formation, and presents challenges in implementing imaging systems that scale in size. We present algorithms, architectures, and abstractions for image formation that relate the different communities, technologies, and tools. We address practical technical challenges in operating millimeter-wave radar and ultrasound systems in the presence of phase noise and scattering. We model a broad class of physical phenomena with isotropic point sources. We show that the optimal source location estimator for coherent waves reduces to processing an image produced by a conventional camera, provided the sources are wellseparated relative to the system resolution, and in the limit of small wavelength and globally incoherent light. We introduce quasi light fields to generalize the incoherent image formation process to coherent waves, offering resolution tradeoffs that surpass the traditional Fourier uncertainty principle by leveraging time-frequency distributions. We show that the number of sensors in a coherent imaging array defines a stable operating point relative to the phase noise. We introduce a digital phase tightening algorithm to reduce phase noise. We present a system identification framework for multiple-input multiple-output (MIMO) ultrasound imaging that generalizes existing approaches with time-varying filters. Our theoretical results enable the application of traditional techniques in incoherent imaging to coherent imaging, and vice versa. Our practical results suggest a methodology for designing millimeter-wave imaging systems. Our conclusions reinforce architectural principles governing transmitter and receiver design, the role of analog and digital circuity, and the tradeoff between data rate and data precision.