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In this paper, we propose a non-linear image enhancement filter for noisy images. Unsharp masking that is widely used for image enhancement amplifies image contrast by adding the high-frequency component that is obtained by a linear high-pass filter from an input image. The linear high-pass filter of the unsharp masking also emphasizes noises that appear in the input image. In order to avoid the emphasis of the noises, weighted unsharp masking techniques have been proposed. In these methods, the high-frequency component is defined as a product between a weighting function of which modulus increases around image edges and the linear high-pass filter output. To improve the noise suppression property of the weighted unsharp masking, we introduce wavelet scale products to the weighting function. The weighting function of the proposed method is defined as the linear combination of the squared of a wavelet transform and the product of the wavelet transforms at different scales. We specify the parameter of the weighting function based on the edge enhancement property and the noise amplification property. The statistical analysis of the noise amplification shows that the proposed method can reduce the noise variance to about 1/5 of the gradient-based weighted unsharp masking filter. Examples of image enhancement and a comparison between the other weighted unsharp masking are also shown.