Noise reduction is an essential step of cDNA microarray image analysis for obtaining better-quality gene expression measurements. Wavelet-based denoising methods have shown significant success in traditional image processing. The complex wavelet transform (CWT) is preferred to the classical discrete wavelet transform for denoising of microarray images due to its improved directional selectivity for better representation of the circular edges of spots and near shift-invariance property. Existing CWT-based denoising methods are not efficient for microarray image processing because they fail to take into account the signal as well as noise correlations that exist between red and green channel images. In this paper, two bivariate estimators are developed for the CWT-based denoising of microarray images using the standard maximum a posteriori and linear minimum mean squared error estimation criteria. The proposed denoising methods are capable of taking into account both the interchannel signal and noise correlations. Significance of the proposed denoising methods is assessed by examining the effect of noise reduction on the estimation of the log-intensity ratio. Extensive experimentations are carried out to show that the proposed methods provide better noise reduction of microarray images leading to more accurate estimation of the log-intensity ratios as compared to the other CWT-based denoising methods.