High-resolution image reconstruction based on multi-band wavelet lifting

High-resolution image reconstruction refers to reconstruction of high-resolution images from multiple low-resolution, shifted, blurred samples of a true image. In this paper, a method based on multi-band wavelet lifting scheme is proposed for high-resolution image reconstruction. By expressing the true image as a square integrable function, Point Spread Function (PSF) can be used to construct biorthogonal and quad-orthogonal wavelet filters directly, thus an iterative algorithm for high-resolution image reconstruction can be derived based on the filters. However, the filters are the piecewise linear spline and corresponding primal and dual wavelet functions are all zero vanishing moments. In order to improve the quality of reconstructed high-resolution images, wavelet lifting scheme is employed to increase the numbers of vanishing moments of wavelet functions so as to improve the performance of the filters. Especially, in order to lift quad-orthogonal wavelet, a lifting scheme for the four-dilation wavelet is given in this paper. Experiment results show that the method can improve the quality of reconstructed high resolution images effectively. At the same time, we derive a fast algorithm that can reconstruct high resolution images efficiently when blurring matrix is block-circulant-circulant-block (BCCB) matrix or Toeplitze-plus-Hankel system with Toeplitze-plus-Hankel block (THTH) matrix.