Abstract: Combining wavelet multi-resolution analysis and the discrete iteration of scalar valued diffusion, a new noisy image zooming model is proposed that presents the original image as the low pass filter of wavelet analysis, and we estimate its high pass filter and use the discrete one iteration of the forward and backward (FAB) diffusion equation to the zoomed image. Because of the threshold of the wavelet coefficients and the property that FAB diffusivity acts as local forward diffusion in the small gradient region, the image is denoised as well as enlarged, and as local backward diffusion in the large gradient region the zoomed image is edge preserved. Some numerical experiments illustrate that not only does the proposed method zooms images, but also the processed images look much clearer and smoother.

Key words: wavelet analysis, scalar-valued diffusion, image zooming, partial differential equations