Super-resolution image reconstruction employing Kriging interpolation technique A. Panagiotopoulou and V. Anastassopoulos Electronics Laboratory, Physics Department University of Patras Rio 26500, Greece Phone: +302610 996147 Fax: +302610 997456 E-mail: vassilis@physics.upatras.gr Keywords: Super-resolution, Subpixel shift, Aliasing, Kriging interpolation, Wiener filter Abstract: In this paper a high-resolution (HR) image is re- constructed from a sequence of subpixel shifted, aliased low- resolution (LR) frames by means of a novel nonuniform in- terpolation super-resolution (SR) method. A gradient-based algorithm estimates the horizontal and vertical shifts for each frame. Then, the uniformly spaced sampling points of the HR image are produced by means of Kriging interpolation. Wie- ner filtering is employed to deal with the restoration problem. The novelty of the proposed nonuniform interpolation ap- proach to SR image reconstruction lies in the employment of Kriging interpolation technique. Comparisons with the origi- nal image demonstrate the superiority of our method to a conventional nonuniform interpolation one of SR image re- construction. 1. INTRODUCTION The employment of signal processing techniques to ob- tain an HR image from multiple observed LR ones is called SR image reconstruction. The goal of SR techniques is the creation of an HR image from several degraded and aliased, subpixel shifted LR images. The present work be- longs to the category of nonuniform interpolation ap- proaches to SR image reconstruction. As soon as the rela- tive motion among the LR frames has been estimated, nonuniform interpolation is applied to produce the uni- formly spaced sampling points of the HR image. Then, res- toration is performed. A nonuniform interpolation approach to SR image re- construction is presented in [1]. A gradient-based registra- tion algorithm calculates the shifts among frames. The frames are placed onto a uniform grid using weighted nearest-neighbor interpolation. Wiener filtering restores the blurred and noisy HR image. A set of aliased images is registered by means of a frequency domain method in [2]. Afterwards, bicubic interpolation is employed to construct an HR image. An SR image reconstruction technique is also presented in [3]. Subpixel shift information is ex- tracted from 1-dimensional characteristic curves and adap- tive subpixel interpolation leads to a uniformly spaced HR grid. Other interpolation techniques which lead to image resolution enhancement have been reported in [7-8]. In this paper an HR image is obtained exploiting the in- formation obtained from 20 subpixel shifted, aliased LR frames. The relative motion between frames is estimated by means of a gradient-based algorithm. Kriging interpola- tion, a method that accepts irregularly spaced data, is em- ployed to construct a uniformly spaced HR grid. It should be stressed that a direct reconstruction procedure is adopted, in contradiction with the employment of iterative procedures often met in the literature. Two different filters are employed to restore the resulting HR image via recur- sive deconvolution procedures. The novelty of the pro- posed approach lies in the employment of Kriging interpo- lation to create the uniformly spaced HR grid after regis- tering the frames. In Section 2 of this paper, Kriging interpolation tech- nique is presented. Section 3 consists of a detailed descrip- tion of the reconstruction procedure, while Section 4 con- tains the results of the conducted experiment. Some deci- sive aspects concerning the presented method are placed in Section 5, whereas conclusions are drawn in Section 6. 2. KRIGING INTERPOLATION Kriging is a geostatistical interpolation technique that considers both the distance and the degree of variation be- tween known data points when estimating values in un- known areas. A kriged estimate is a weighted linear com- bination of the known sample values around the point to be estimated. The unknown value of the signal y x f f , 0 at a given coordinate position is expressed as 0 0 , y x S s s s s y x f w y x f 1 , , 1 where S is the number of the known sample values of the signal. Kriging attempts to minimize the error variance and set the mean of the prediction errors to zero. Before the ac- tual interpolation can begin, Kriging must calculate every possible distance weighting function. This is done by gen- erating the experimental semivariogram of the data set and choosing a mathematical model which best approximates the shape of the semivariogram [4]. In our case, a Gaussian model is used (see Fig. 1). A smooth, continuous function for determining appropriate weights for increasingly dis- tant data points is provided by the model. A semivariogram is a graph which plots the semivariance be- tween points on the Y-axis and the distance at which the semivariance was calculated on the X-axis. The semivari- ance is one half the average squared difference of data val- ues spaced a constant distance apart. As points are com- pared to increasingly distant points, the semivariance in- creases. At some distance, the semivariance will become approximately equal to the variance of the whole surface itself. This is the greatest distance over which the value at a point on the surface is related to the value at another point. This surface variance criterion leads to the selection of the appropriate known data points when estimating the value of an unknown point. 978-961-248-029-5/07 © 2007 UM FERI 2007 IWSSIP & EC-SIPMCS, Slovenia 151