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Development of efficient fusion algorithms is becoming increasingly important for obtaining a more informative image from several source images captured by different modes of imaging systems or multiple sensors. Since noise is inherent in practical imaging systems or sensors, an integrated approach of image fusion and noise reduction is essential. The discrete wavelet transform has been significantly successful in the development of fusion algorithms for noise-free images as well as in image denoising algorithms. A novel contrast-based image fusion algorithm is proposed in the wavelet domain for noisy source images. Novel features of the proposed fusion method are the noise reduction taking into consideration the linear dependency among the noisy source images and introducing an appropriate modification of the magnitude of the wavelet coefficients depending on the noise strength. Experiments are carried out on a number of commonly-used greyscale and colour test images to evaluate the performance of the proposed method. Results show that the performance of the proposed fusion method is better than that of other methods in terms of several frequently-used metrics, such as the structural similarity, peak signal-to-noise ratio and cross-entropy, as well as in the visual quality, even in the case of correlated noise.