Considering that Double-density dual-tree(DD-DT)complex wavelet has translation invariance, anti-aliasing properties and more compact space intervals, based on the quantum-inspired parameter estimation, this paper proposed a new quantum-inspired noise reduction method based on DD-DT complex wavelet transform for remote sensing images, especially the SAR images. The general process is addressed as below: conduct a logarithmic transformation for the SAR images, convert the multiplicative speckle noises to additive noises; then decompose the DD-DT complex wavelets for each image, thus to get the wavelet coefficient for each layer in all detailed directions; consider the inter-scale correlation of wavelet coefficient, utilize the Bayesian estimation theory along with the quantum mechanics principle of superposition, calculate the estimated wavelet coefficient; and then process the data layer by layer, refactor the SAR images using the processed coefficients. Then conduct a anti-logarithmic transformation to get the noise reduction result. Compare with the results of traditional methods, the resulting images have a significant improvement in different evaluation functions such as the Peak Signal Noise Ratio, Edge Preserve Index etc. The results have also shown better noise reduction quality in the images.