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Abstract: A Wavelet is a function in $L_2$ whose dialations and translations form an orthonormal basis of $L_2$. In image processing, it is well known that edges of an image can be detected by using Wavelet Transformation. If the orthonormal condition in the defintion of a Wavelet is dropped, the corresponding function is called a Wavelet Frame. I will talk about construction of box spline tight wavelet frames, and apply this wavelet frames to several images for edge detection. The edge detection using box spline tight wavelet frames will be compared with the edge detection using Haar wavelet, Daubechies' wavelet and Laplacian method. I will show the numerical evidence that the edge detection of smooth curve part of images by box spline tight frames works better than edge detection with the other methods mentioned above.
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