High-resolution Image Reconstruction And Its Fast Algorithm

In this paper, a method based on wavelet and 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 wavelet filters directly, thus an iterative algorithm for high-resolution image reconstruction can be derived based on the filters. 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, wavelet lifting scheme is employed to increase the numbers of vanishing moments of wavelet functions so as to improve performance of the biorthogonal filters. For 4times4 sensor arrays, we can get a 4-dilation wavelet. In this paper, wavelet lifting scheme for four-band wavelet is derived and applied to high-resolution image reconstruction. Experiment results show that the method can improve the quality of reconstructed high resolution images effectively. Also, the method can easily be extended to super-resolution case. 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

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