Performance of reconstruction-based super-resolution with regularization

Authors:
Minmin Shen;Ci Wang;Ping Xue;Weisi Lin
Affiliations:
Nanyang Technological University, 639798 Singapore, Singapore;Nanyang Technological University, 639798 Singapore, Singapore and Shanghai Jiao Tong University, 800 Dongchuan Road, Min Hang, Shanghai 200240, China;Nanyang Technological University, 639798 Singapore, Singapore;Nanyang Technological University, 639798 Singapore, Singapore
Venue:
Journal of Visual Communication and Image Representation
Year:
2010

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Abstract

From the perspective of linear algebra, the performance of super-resolution reconstruction (SR) depends on the conditioning of the linear system characterizing the degradation model. This is analyzed in the Fourier domain using the perturbation theory. By proposing a new SR error bound in terms of the point spread function (PSF), we reveal that the blur function dominates the condition number (CN) of degradation matrix, and the advantage of non-integer magnification factors (MFs) over the integer ones comes from sampling zero crossings of the DFT of the PSF. We also explore the effect of regularization by integrating it into the SR model, and investigate the influence of the optimal regularization parameter. A tighter error bound is derived given the optimal regularization parameter. Two curves of error bounds vs. MFs are presented, and verified by processing real images. It explains that with proper regularization, SR at the integer MFs is still valid.