  We develop a new compressive sensing (CS) inversion algorithm by utilizing
the Gaussian mixture model (GMM). While the compressive sensing is performed
globally on the entire image as implemented in our lensless camera, a low-rank
GMM is imposed on the local image patches. This low-rank GMM is derived via
eigenvalue thresholding of the GMM trained on the projection of the measurement
data, thus learned {\em in situ}. The GMM and the projection of the measurement
data are updated iteratively during the reconstruction. Our GMM algorithm
degrades to the piecewise linear estimator (PLE) if each patch is represented
by a single Gaussian model. Inspired by this, a low-rank PLE algorithm is also
developed for CS inversion, constituting an additional contribution of this
paper. Extensive results on both simulation data and real data captured by the
lensless camera demonstrate the efficacy of the proposed algorithm.
Furthermore, we compare the CS reconstruction results using our algorithm with
the JPEG compression. Simulation results demonstrate that when limited
bandwidth is available (a small number of measurements), our algorithm can
achieve comparable results as JPEG.

Machine Learning;Machine Learning;Applications