This thesis proposes a structure of a two-dimensional adaptive digital filter for the cancellation of white Gaussian noise and edge preservation in images. This structure is composed of three parts. We use a two-dimensional filtering algorithm to avoid the disturbance due to one-dimensional filtering, a neural network to update the filter coefficients, and a variable-size filtering window to preserve edges. Experimental results show that a filter with the proposed two-dimensional structure cancels the white Gaussian noise and preserves the edges of the image better than those filters based on a one-dimensional filtering algorithm or which do not consider the edges.
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