A statistical unification of image interpolation, error concealment, and source-adapted filter design

Author(s):  
M. Muhlich ◽  
R. Mester
Author(s):  
Carlo Ciulla

The intent of the present chapter is to expand the treatise that concerns with the presentation of the current literature in signal-image interpolation with specific focus on the classification of the procedures and the relevant applications of interpolation, in relationship to the various scientific disciplines. Also, the present chapter expands on the importance of the error bounds existing in literature for the characterization and quantification of the interpolation error. The discussion is interleaved with the characteristics features of the unifying theory that the book presents such to place the SRE-based interpolation functions within the context of the larger framework that the scientific literature has conceived so far.


Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 206 ◽  
Author(s):  
Xiao Zhou ◽  
Chengyou Wang ◽  
Zhi Zhang ◽  
Qiming Fu

Based on a deep understanding of all-phase digital filter (APDF) design and all-phase biorthogonal transform (APBT), this paper will further study the windowed all-phase digital filter (WAPDF) and windowed all-phase biorthogonal transform (WAPBT), discuss the principle of the WAPBT, and provide a unified construction method of the all-phase transform (APT). Based on a type of orthogonal transform, i.e., discrete sine transform (DST), an interpolation filter called an all-phase DST (APDST) filter is constructed and used for image demosaicking; it is compared with bilinear interpolation and all-phase inverse discrete cosine transform (APIDCT) interpolation filters, to test its performance in image interpolation and provide analysis and discussion. The experimental results show that APIDCT and APDST filters with a size of 7 × 7 are similar in interpolation performance, but better than the bilinear interpolation method. In addition to its use in image interpolation demosaicking, the low-pass filter designed in this paper can also be widely used in image interpolation, image denoising, image resizing, and other fields of image processing.


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