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This paper describes a new method for contrast enhancement in images of low-light or unevenly illuminated scenes based on statistical modelling of wavelet coefficients of the image. A non-linear enhancement function has been designed based on the local dispersion of the wavelet coefficients modelled as a bivariate Cauchy distribution. Within the same statistical framework, a simultaneous noise reduction in the image is performed by means of a shrinkage function, thus preventing noise amplification. The proposed enhancement method has been shown to perform very well with insufficiently illuminated and noisy images, outperforming other conventional methods, in terms of contrast enhancement and noise reduction in the output image.