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This paper is concerned with a classical denoising and deblurring problem in image recovery. Our approach is based on a variational method. By using the Legendre­Fenchel transform, we show how the nonquadratic criterion to be minimized can be split into a sequence of half-quadratic problems easier to solve numerically. First we prove an existence and uniqueness result, and then we describe the algorithm for computing the solution and we give a proof of convergence. Finally, we present some experimental results for synthetic and real images. [ABSTRACT FROM AUTHOR]