Guaranteed reconstruction for image super-resolution

This paper presents a new reconstruction operator to be used in a super-resolution scheme. Here, by reconstruction in super-resolution, we mean the back-projection operation, i.e. the way K low resolution (LR) images are aggregated to obtain a smooth high resolution (HR) image. Within this method, we replace the usual reconstruction procedure by a non-additive reconstruction operation based on the nice properties of fuzzy partitions. This non-additive reconstruction operator represents a convex family of usual additive reconstruction operators. The obtained reconstructed image is thus a convex family of usual reconstructed images. It allows the super-resolution method to be less sensitive to the choice of the reconstruction method. To make the reading of this method easier, it is presented with 1D signals. We present some experiments to illustrate the proved properties of this new operator.

[1]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.

[2]  Wen-Yu Su,et al.  Recursive high-resolution reconstruction of blurred multiframe images , 1993, IEEE Trans. Image Process..

[3]  Peyman Milanfar,et al.  Super-resolution imaging , 2011 .

[4]  Sébastien Destercke,et al.  Filtering with clouds , 2012, Soft Comput..

[5]  H. Stark,et al.  Convex projections in image processing , 1990, IEEE International Symposium on Circuits and Systems.

[6]  Michael Unser,et al.  B-spline signal processing. I. Theory , 1993, IEEE Trans. Signal Process..

[7]  Michal Irani,et al.  Improving resolution by image registration , 1991, CVGIP Graph. Model. Image Process..

[8]  Kevin Loquin,et al.  Possibilistic signal processing: How to handle noise? , 2010, Int. J. Approx. Reason..

[9]  Enrique H. Ruspini.  New experimental results in fuzzy clustering , 1973, Inf. Sci..

[10]  Michal Irani,et al.  Motion Analysis for Image Enhancement: Resolution, Occlusion, and Transparency , 1993, J. Vis. Commun. Image Represent..

[11]  M. Sezan,et al.  Image Restoration by the Method of Convex Projections: Part 2-Applications and Numerical Results , 1982, IEEE Transactions on Medical Imaging.

[12]  Akram Aldroubi,et al.  B-spline signal processing. II. Efficiency design and applications , 1993, IEEE Trans. Signal Process..

[13]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[14]  Akram Aldroubi,et al.  B-SPLINE SIGNAL PROCESSING: PART II-EFFICIENT DESIGN AND APPLICATIONS , 1993 .

[15]  D. Denneberg.  Non-additive measure and integral , 1994 .

[16]  Roger Y. Tsai,et al.  Multiframe image restoration and registration , 1984 .

[17]  Kai-Kuang Ma,et al.  A survey on super-resolution imaging , 2011, Signal Image Video Process..

[18]  Vivek Bannore.  Iterative-Interpolation Super-Resolution (IISR) , 2009 .

[19]  Kevin Loquin,et al.  On the granularity of summative kernels , 2008, Fuzzy Sets Syst..

[20]  Kevin Loquin,et al.  Histogram density estimators based upon a fuzzy partition , 2008 .

[21]  H Stark,et al.  High-resolution image recovery from image-plane arrays, using convex projections. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[22]  Gert de Cooman.  Integration and Conditioning in Numerical Possibility Theory , 2004, Annals of Mathematics and Artificial Intelligence.

[23]  Michal Irani,et al.  Super resolution from image sequences , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[24]  Peter Walley,et al.  Towards a unified theory of imprecise probability , 2000, Int. J. Approx. Reason..

[25]  Akram Aldroubi,et al.  B-SPLINE SIGNAL PROCESSING: PART I-THEORY , 1993 .

[26]  Kevin Loquin,et al.  Linear filtering and mathematical morphology on an image: A bridge , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[27]  A. Murat Tekalp,et al.  Super resolution recovery for multi-camera surveillance imaging , 2003, 2003 International Conference on Multimedia and Expo. ICME '03. Proceedings (Cat. No.03TH8698).

[28]  S. Chaudhuri.  Super-Resolution Imaging , 2001 .

[29]  H. Stark,et al.  Theory of convex projection and its application to image restoration , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[30]  Nirmal K. Bose,et al.  Recursive reconstruction of high resolution image from noisy undersampled multiframes , 1990, IEEE Trans. Acoust. Speech Signal Process..