Variational PDE Techniques in Wavelet Based Image Compression

Hao-Min Zhou (Georgia Institute of Technology)
(Joint work with Prof. Tony Chan at UCLA)

In digital image processing, information is lost or damaged due
to compression or transmission. Image qualities are degraded, specially
around the edges such as the edge artifacts. To recover the information,
regularizations are often used. In this talk, we use Partial Differential
Equation (PDE) techniques in wavelet based image processing to reduce
edge artifacts generated by wavelet thresholding. We employ a variational
framework, in particular the minimization of total variation (TV) as the
regularization, to select and modify the retained standard wavelet
coefficients so that the reconstructed images have fewer oscillations
near edges. Numerical experiments show that this approach improves the
reconstructed image quality in wavelet compression and in denoising.


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