Sparse image measurement with an optical single-pixel detector using various schemes of image sampling

We present the theoretical and experimental results of computational ghost imaging using compressive sensing. Our particular interest lies in imaging medical structures in depth of the tissue, compressible in either wavelet or Fourier domain. The measurement is based on a sequence of images from a bucket detector. We establish the optimal measurement and reconstruction basis in order to obtain the best quality of the image reconstruction with possibly few measurements. We consider several schemes of image sampling based on orthonormal basis incoherent either with the Fourier basis or with Daubechies wavelet sets, such as orthonormalised Gaussian random matrices, Hadamard matrices and noiselet matrices. Eventually, the optimal sampling scheme has been introduced into the experimental single-pixel camera set-up for imaging in the visible wavelength range.