A diffusion process for wavelet-transform-based image denoising and its application to document image binarization

Wavelet based image denoising methods have attracted extensive interests over the last decade. Donoho et. al. [3] first suggested to remove/suppress noise by thresholding of wavelet coefficients. The underlying assumption is simple and intuitive: a wavelet coefficient is treated as noise and set to zero if it is below a preset threshold. Otherwise, the coefficient is kept or slightly modified. To estimate threshold as accurate as possible, numerous (non/)adaptive schemes have been proposed (see e.g. [1][2]). While the Wavelet Transform-ThresholdInverseTransform (WTTI) methods have been successful over extensive tests, the assumption that one can distinguish noise from signal solely based on coefficient magnitudes is violated when noise levels are higher than signal magnitudes. Under this high noise circumstance, the spatial configuration of neighboring wavelet coefficients can play an important role in noise-signal classifications. Signals tend to form meaningful features (e.g. straight lines, curves), while noisy coefficients often scatter randomly. In the present work, we exploit this spatial correlation of wavelet coefficients, combined with coefficient magnitudes, to classify and suppress noisy coefficients. In particular, we propose to replace the second step of the Wavelet Transform-Thresholding-InverseTransform (WTTI) methods with a diffusion process, which iteratively modifies wavelet coefficients such that the consistency among neighboring coefficients is maximized (Section 2.1). In Section 3, we apply both a WTTI method and the proposed Wavelet Transform-Diffusion-InverseTransform (WTDI) method to document image binarization. Experimentally, we demonstrate that the WTDI method is more robust to high noise levels.