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A speckle suppression method for medical ultrasound images is proposed by combining the dual-tree complex wavelet transform (DTCWT) with a new quantum-inspired adaptive threshold function. An adaptive non-Gaussian statistical model is proposed for the complex wavelet coefficients. According to products of the coefficients and their parents in multi-scale subbands, the quantum-inspired probability of noise is considered in the proposed threshold function. Experiments demonstrate the effectiveness of the proposed method.