Dual-space Compressed Sensing

Compressed sensing (CS) is routinely utilized to accelerate sampling processes, and attempts have been made to employ it into quantum sensing and quantum information processing. Here we present a dual-space CS approach that is suited for application of dual-mode imaging of nanodiamonds, combining optical imaging and dynamical nuclear polarization (DNP) enhanced magnetic resonance imaging [1]. This novel CS regime harnesses the ability to sample in two Fourier reciprocal spaces (e.g. k- and x-space) simultaneously. In contrast to conventional CS that only samples in single k-space, we show that dual-space CS offers significant acceleration in imaging speed and enhancement in robustness to noise. We will also describe its application towards edge detection. This work suggests a way to strategically sample two incoherent spaces to gain imaging acceleration, and can be generalized to images sampled over multiple uncorrelated spaces. Application of these ideas to quantum sensing will be discussed.

 

[1] Lv, Xudong, et al. "Background-free dual-mode optical and 13C magnetic resonance imaging in diamond particles." Proceedings of the National Academy of Sciences 118.21 (2021).