Compressive Ghost Imaging with Customized Speckles

Speckle patterns arise when coherent light reflects from rough surfaces or propagates through complex scattering media, such as disordered materials or multimode fibers. These patterns exhibit a random granular structure, with their statistical properties typically following Rayleigh statistics. The probability density function (PDF) of the complex field conforms to a circular Gaussian distribution, while the intensity PDF follows a negative exponential distribution. Wavefront shaping techniques can modify these statistical properties by controlling wavefront intensity, polarization, or phase [1], enabling diverse applications, including advanced imaging, cryptography, and optical communications. Compressive ghost imaging (CGI) leverages speckle patterns for image reconstruction using a bucket detector instead of a traditional camera [2]. This technique relies on compressive sensing, which exploits object sparsity to achieve accurate image reconstruction with fewer measurements. CGI is particularly advantageous in challenging environments, such as imaging through highly scattering or dynamic media.