Abstract : It was shown recently that the phase of the Fourier Transform of an image could lead to interesting no-reference image quality measures. The Global Phase Coherence, and its recent Gaussian variant called Sharpness Index, rate the sharpness of an image in contrast not only with blur, but also noise, ringing, etc. In this work, we introduce a new variant of these indices, that can be computed with one Fourier Transform only, hence four times quicker than the Sharpness Index. We use this new index S to build an image restoration algorithm that, in a stochastic framework, selects a radial-unimodal deconvolution kernel for which the S-value of the restored image is optimal. Experiments are discussed, and comparison is made with a radial oracle deconvolution filter and the recent blind deconvolution algorithm of Levin et al.