High-resolution image reconstruction using wavelet lifting scheme

High-resolution image reconstruction refers to reconstruction of high-resolution images from multiple low-resolution, shifted, blurred samples of a true image. By expressing the true image as a square integrable function, Point Spread Function (PSF) can be used to construct biorthogonal wavelet filters directly and some algorithms for high-resolution image reconstruction were proposed based on the filters. However, the filters are the piecewise linear spline and corresponding primal and dual wavelet functions are all one vanishing moments. In order to improve the quality of reconstructed high-resolution images, we propose a method in this paper which can increase the numbers of vanishing moments of the wavelet functions so as to improve the performance of the biorthogonal filters using wavelet lifting scheme. Experiment results show that the method can improve the quality of reconstructed high-resolution images effectively. Also, 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.