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Tele-dermatology is becoming an important tool for early skin cancer detection in public health, but low-cost cameras tend to cause image blurring, which affect diagnosis quality. Obtaining cost-effective images with diagnosis quality is a current challenge, and this paper proposes a novel method for enhancing the local contrast of dermatological images in the wavelet domain. The distribution of squared gradient magnitudes computed through an undecimated wavelet transform is modeled as a combination of chi-squared and gamma distributions, and a posteriori probabilities are used to discriminate coefficients related to edges from those related to noise or homogeneous regions at each scale of the wavelet decomposition. Consistency across scales is used to preserve coefficients likely to be edge related in consecutive levels of the wavelet decomposition, and local directional smoothing is used to reduce residual noise. Then, a nonlinear enhancement function is applied to wavelet coefficients, so that low-contrast edge-related wavelet coefficients are increased. Our experimental results indicate that the proposed approach can effectively sharpen image details, without amplifying background noise. Preliminary validation by specialists indicate that the proposed sharpening algorithm improves the visual quality of dermatological images.