On a compact non-extrapolating scheme for adaptive image interpolation

Abstract The motivation of this paper is to improve the results of ENO subcell resolution, that already obtains really good results but using extrapolation, as was stated by F. Arandiga, R. Donat and P. Mulet [Adaptive Interpolation of Images, Signal Processing 83(2) (2003) 459–464]. We present a new method for image interpolation which combines a new nonlinear cell-average interpolatory technique that uses a trigonometric mean and subcell resolution. The scheme uses a fully compact reconstruction and avoid any step of extrapolation. The experiments presented validate the theoretical results obtained.

[1]  A. Cohen,et al.  Quasilinear subdivision schemes with applications to ENO interpolation , 2003 .

[2]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[3]  Basarab Matei.  Smoothness characterization and stability in nonlinear multiscale framework: theoretical results , 2005 .

[4]  Sergio Amat,et al.  Data Compression with ENO Schemes: A Case Study☆☆☆ , 2001 .

[5]  Pep Mulet,et al.  Adaptive interpolation of images , 2003, Signal Process..

[6]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[7]  Nira Dyn,et al.  Adaptive Approximation of Curves , 2004 .

[8]  Richard Baraniuk,et al.  Multiscale Approximation of Piecewise Smooth Two-Dimensional Functions using Normal Triangulated Meshes , 2005 .

[9]  P. Oswald,et al.  Stability of Nonlinear Subdivision and Multiscale Transforms , 2010 .

[10]  A. Harten.  Multiresolution representation of data: a general framework , 1996 .

[11]  I. Daubechies,et al.  Normal Multiresolution Approximation of Curves , 2004 .

[12]  Theoretical, Applied and Computational Aspects of Nonlinear Approximation , 2003 .

[13]  Jacques Liandrat,et al.  Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms , 2011, Adv. Comput. Math..

[14]  Peter Oswald.  Smoothness of Nonlinear Median-Interpolation Subdivision , 2004, Adv. Comput. Math..

[15]  Albert Cohen,et al.  Tensor product multiresolution analysis with error control for compact image representation , 2002, Signal Process..

[16]  Francesc Aràndiga,et al.  Nonlinear multiscale decompositions: The approach of A. Harten , 2000, Numerical Algorithms.

[17]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[18]  A. Harten.  ENO schemes with subcell resolution , 1989 .

[19]  Jacques Liandrat,et al.  Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing , 2006, Found. Comput. Math..