Quantitative effects of discrete wavelet transforms and wavelet packets on aerial digital image denoising

The objective of image denoising is to remove the noises and to retain important image features as much as possible. Linear approaches could be effective for some simple cases with slowly varying noises, but not for other slowly varying noise cases and rapidly varying noise cases. As a nonlinear wavelet based technique, the wavelet thresholding is effective to denoise blurring aerial images. Either the discrete wavelet transform or wavelet packets technique can be employed using wavelet decomposition. At each level of wavelet decompositions, the digital image is split into four subbands, representing approximation (low frequency feature) and three details (high frequency features) in horizontal, vertical and diagonal directions. The proposed soft thresholding wavelet decomposition at multiple levels is a simple and efficient method for reduction of noises. For multiple level decompositions in terms of both the discrete wavelet transform and wavelet packets techniques, the approximation component will always be decomposed at each level. If the detail components are further decomposed as well similar to that of the approximation, it is the wavelet packet approach, otherwise it is the discrete wavelet transform. On a basis of the proposed thresholding technique at different levels for wavelet denoising, objective metrics can be introduced also to evaluate and compare the denoising effects of the discrete wavelet transform and wavelet packets quantitatively rather than qualitative observation, such as the metrics of the discrete entropy, energy and mutual information.