An original method to denoise ultrasonic images affected by speckle is presented. Speckle is modeled as a signal-dependent noise corrupting the image. Noise reduction is approached as a Wiener-like filtering performed in a shift-invariant wavelet domain by means of an adaptive rescaling of the coefficients of an undecimated octave decomposition. The scaling factor of each coefficient is calculated from local statistics of the degraded image, the parameters of the noise model, and the wavelet filters. Experimental results demonstrate that excellent background smoothing as well as preservation of edge sharpness and fine details can be obtained.