# Super-Resolution Remote Imaging Using Time Encoded Remote Apertures
## 1 Introduction  
### Previous Attempts to Beat the Diffraction Limit of Resolution  
The diffraction limit naturally limits the spatial resolution of an image acquired by a conventional imaging system with a finite aperture. A wave traveling from the scene to the imaging system is subject to diffraction. The wave reaching the aperture of the imaging system has been degraded by diffraction. It can no longer be used to reconstruct an image of the object at the optimal resolution. Any spatial wavefront is subject to this diffraction, which causes a well-known linear drop in resolution with distance. The resulting linear dependence of resolution on imaging distance is known as the Rayleigh criterion.  
Over the last several years, many works in different fields have been done to beat the diffraction limit. Astronomical imaging is an area where super-resolution methods are extensively studied. Most of the super-resolution methods used in astronomy combine image capturing techniques with image post-processing. In early years, co-addition methods, capturing successively multiple pictures within a short exposure time and applying shift-and-add algorithm [1] or linear reconstruction scheme [2] to combine the images, were actively used. Different regularization-based optimization methods were developed: [PERSON] et al. [3] successfully applied quadratic-regularized optimization to the \"Spectral and Photometric Imaging Receiver\" data. [PERSON] et al. [4] demonstrated the high-resolution fluorescence microscopy method (STORM) that utilizes high-accuracy localization of photoswitchable fluorophores. The method operates past the diffraction limit. [PERSON] et al. [5] proposed a method using a deconvolution technique, maximum correlation method, combined with a re-sampling kernel to super-resolve \"Wide-field Infrared Survey Explorer\" data.  
Several image post-processing methods exist in digital imaging applications in order to construct high-resolution images from low-resolution images. Nonuniform interpolation approach [6],frequency domain approach [7], regularized optimizations (deterministic [8; 9; 10; 11] and stochastic [12; 13; 14; 15]), iterative back-projection [16], adaptive filtering approach [17] are widely used super-resolution imaging methods. These super-resolution methods provide high-resolution image outputs, mitigating the effects of diffraction. However, all of the methods still suffer from the fundamental limit: the resolution of super-resolved images still depends on the distance and aperture of the imaging system. The further the region of interest, the lower the image resolutions.  
It is well known that a scattering medium around an object can be used to couple evanescent waves into the far-field. This means that images of the embedded object with resolutions similar to the wavelength can be captured from large distances [18]. In existing approaches, this requires prior characterization of the scattering medium from the location of the object, which makes the method unsuitable for many practical applications. Here, we show that scattering can be leveraged in sparse scenes to determine the geometry of the entire scattering scene (object and medium) without prior information based on just a single pixel time response of the scene.