Single-Shot Compressed Imaging via Random Phase Modulation

Compressed sensing (CS) provides an innovative framework for signal sampling, which enables accurate recovery of the sparse or compressible signal from a small set of linear measurements far fewer than the Nyquist rate in traditional signal processing. In compressed sensing, random modulation plays a key role, which can spread out the signal information more or less evenly across all locations. There are many modulation techniques, such as amplitude modulation, frequency modulation, phase modulation, spectrum modulation, and so on. Among these modulation techniques, phase modulation is vital due to the efficiency and convenience of modulation. In this paper, we review both the theoretical and application of compressed sensing and several compressed imaging systems using random phase modulation. First, we review the fundamentals of compressed sensing, dividing it into three parts: sparse representation, incoherent measurement, and nonlinear reconstruction algorithm. We then show how phase modulation can be applied to compressed sensing and compressed imaging, where the presentation can be divided into six main parts, corresponding to different aspects of phase modulation applied in compressed sensing or compressed imaging: (1) Fundamentals of compressed sensing. (2) Principles of phase modulation. (3) Single-shot compressed imaging with spatial-domain single random phase mask (CI-SSRPM). (4) Single-shot compressed imaging with a random convolution using a double random phase mask (CI-DRPM). (5) Single-shot compressed imaging with Fourier-domain single random phase mask (CI-FSRPM). (6) Single-shot compressed imaging with double random phase encoding (CI-DRPE).