Combined transform image denoising based on morphological component analysis

Wavelet transform is well suited for the effective (sparse) representation of the image smooth region. Curvelet transform can get better approximation of the linear singular for two-dimensional or higher-dimensional function, and is the sparsest representation for the image with linear singular part and the edge region. This paper proposes a combined transform image denoising algorithm based on morphological component analysis (MCA). The MCA method is used to separate the image into natural scene and linear singular structure. Curvelet transform threshold denosing is used in linear singular structure while wavelet transform deals with smooth part. This algorithm makes full use of respective advantages of the wavelet transform and curvelet transform. Experiment results show that the algorithm can better maintain the details characteristics in dealing with the image with linear singularity, and it has a better denosing performance for image than a simple wavelet thresholding or curvelet thresholding.