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This paper presents a novel speckle suppression method for medical B-scan ultrasonic images. An original image is first separated into two parts with an adaptive filter. These two parts are then transformed into a multiscale wavelet domain and the wavelet coefficients are processed by a soft thresholding method, which is a variation of Donoho's (1995) soft thresholding method. The processed coefficients for each part are then transformed back into the space domain. Finally, the denoised image is obtained as the sum of the two processed parts. A computer-simulated image and an in vitro B-scan image of a pig heart have been used to test the performance of this new method. This technique effectively reduces the speckle noise, while preserving the resolvable details. It performs well in comparison to the multiscale thresholding technique without adaptive preprocessing and two other speckle-suppression methods.