Optimal Dictionaries for Sparse Solutions of Multi-frame Blind Deconvolution

Abstract: Sparse representation of data has grown rapidly in signal processing. The benefits of sparse regularization are economy of representation of many different varieties of data, as well as control of difficult aspects of inverse problems, e.g., regularization of ill-conditioned inverse problems. Herein we represent atmospheric turbulence point-spread-functions by training optimal overcomplete dictionaries from atmospheric turbulence data. Implications for blinddeconvolution of turbulent images are discussed. The application of sparse dictionaries is demonstrated by the employment of sparse PSF representations to formulate a multi-frame blind deconvolution (MFBD) algorithm. We present results of the gain in MFBD image reconstruction by simulations of turbulent atmospheric images and the reconstruction of the corresponding images with the sparse PSF MFBD algorithm. Sparse representation of data has grown rapidly in signal processing. The benefits of sparse regularization are economy of representation of many different varieties of data, as well as control of difficult aspects of inverse problems, e.g., regularization of ill-conditioned inverse problems. Herein we represent atmospheric turbulence point-spread-functions by training optimal overcomplete dictionaries from atmospheric turbulence data. Implications for blinddeconvolution of turbulent images are discussed. The application of sparse dictionaries is demonstrated by the employment of sparse PSF representations to formulate a multi-frame blind deconvolution (MFBD) algorithm. We present results of the gain in MFBD image reconstruction by simulations of turbulent atmospheric images and the reconstruction of the corresponding images with the sparse PSF MFBD algorithm.