Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Restoration of Astrophysical Images—The Case of Poisson Data with Additive Gaussian Noise | EURASIP Journal on Applied Signal Processing 2005 15 2500-2513 2005 Hindawi Publishing Corporation Restoration of Astrophysical Images The Case of Poisson Data with Additive Gaussian Noise H. Lanteri Laboratoire d Astrophysique Universite de Nice Sophia Antipolis CNRS UMR6525 06108 Nice Cedex 2 France Email hlanteri@ Laboratoire d Astrophysique Universite de Nice Sophia Antipolis CNRS UMR6525 06108 Nice Cedex 2 France Email Received 28 May 2004 Revised 28 October 2004 We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity then a Gaussian white noise is added during the electronic read-out operation. We show first that the split gradient method SGM previously proposed can be used to obtain maximum likelihood ML iterative algorithms adapted in such noise combinations. However when ML algorithms are used for image restoration whatever the noise process is instabilities due to noise amplification appear when the iteration number increases. To avoid this drawback and to obtain physically meaningful solutions we introduce various classical penalization-regularization terms to impose a smoothness property on the solution. We show that the SGM can be extended to such penalized ML objective functions allowing us to obtain new algorithms leading to maximum a posteriori stable solutions. The proposed algorithms are checked on typical astronomical images and the choice of the penalty function is discussed following the kind of object. Keywords and phrases restoration astronomic images Poisson transformation MAP estimation regularization iterative algorithms. 1. INTRODUCTION The image restoration problem and particularly image deconvolution is an inverse problem ill posed in the sense of Hadamard whose
