Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.Comment: 16 page

Super-resolution far-field ghost imaging via compressive sampling

Much more image details can be resolved by improving the system's imaging resolution and enhancing the resolution beyond the system's Rayleigh diffraction limit is generally called super-resolution. By combining the sparse prior property of images with the ghost imaging method, we demonstrated experimentally that super-resolution imaging can be nonlocally achieved in the far field even without looking at the object. Physical explanation of super-resolution ghost imaging via compressive sampling and its potential applications are also discussed.Comment: 4pages,4figure

Exploiting flow dynamics for super-resolution in contrast-enhanced ultrasound

Ultrasound localization microscopy offers new radiation-free diagnostic tools for vascular imaging deep within the tissue. Sequential localization of echoes returned from inert microbubbles with low-concentration within the bloodstream reveal the vasculature with capillary resolution. Despite its high spatial resolution, low microbubble concentrations dictate the acquisition of tens of thousands of images, over the course of several seconds to tens of seconds, to produce a single super-resolved image. %since each echo is required to be well separated from adjacent microbubbles. Such long acquisition times and stringent constraints on microbubble concentration are undesirable in many clinical scenarios. To address these restrictions, sparsity-based approaches have recently been developed. These methods reduce the total acquisition time dramatically, while maintaining good spatial resolution in settings with considerable microbubble overlap. %Yet, non of the reported methods exploit the fact that microbubbles actually flow within the bloodstream. % to improve recovery. Here, we further improve sparsity-based super-resolution ultrasound imaging by exploiting the inherent flow of microbubbles and utilize their motion kinematics. While doing so, we also provide quantitative measurements of microbubble velocities. Our method relies on simultaneous tracking and super-localization of individual microbubbles in a frame-by-frame manner, and as such, may be suitable for real-time implementation. We demonstrate the effectiveness of the proposed approach on both simulations and {\it in-vivo} contrast enhanced human prostate scans, acquired with a clinically approved scanner.Comment: 11 pages, 9 figure