OPTIMAL LINEAR INTERPOLATION OF IMAGES WITH KNOWN POINT SPREAD FUNCTION

The need for interpolation between pixels arises in many contexts. Kriging provides a general theory for optimal linear interpolation, which can be implemented and interpreted in either spatial or frequency domains. Of critical importance is knowledge of the autocorrelation function of the image at sub-pixel distances or, equivalently, the form of the spectrum near the Nyquist frequency. Although neither of these will typically be known, in many applications the point spread function of the imaging sensor is either known or can be estimated. We show how this knowledge can be combined with an assumption that the true scene is a Matern process, to derive a linear interpolant with minimum variance which takes account of the effects of aliasing in the sampled image. We apply the new method to both simulated and X-ray computed tomography images, and show it to be superior to bicubic and sinc interpolation for images that are not band-limited at the Nyquist frequency.

[1]  Thomas Martin Deserno,et al.  Survey: interpolation methods in medical image processing , 1999, IEEE Transactions on Medical Imaging.

[2]  K. Mardia,et al.  A penalized likelihood approach to image warping , 2001 .

[3]  J. R. Wallis,et al.  An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields , 1994 .

[4]  Mark Berman,et al.  Estimating Band-to-Band Misregistrations in Aliased Imagery , 1994, CVGIP Graph. Model. Image Process..

[5]  P. Whittle.  The Analysis of Multiple Stationary Time Series , 1953 .

[6]  Inge Sandholt.  N.A.C. Cressie: Statistics for spatial data. , 1993 .

[7]  K. Mardia,et al.  A review of image-warping methods , 1998 .

[8]  Chris A. Glasbey,et al.  Estimation of tissue proportions in X-ray CT images using a new mixed pixel distribution , 1999 .

[9]  E. Maeland.  On the comparison of interpolation methods. , 1988, IEEE transactions on medical imaging.

[10]  Chris A. Glasbey,et al.  BINARY IMAGE RESTORATION AT SUBPIXEL RESOLUTION , 1997 .

[11]  Dimitris Anastassiou,et al.  Subpixel edge localization and the interpolation of still images , 1995, IEEE Trans. Image Process..

[12]  Rob W. Parrott,et al.  Towards statistically optimal interpolation for 3D medical imaging , 1993, IEEE Engineering in Medicine and Biology Magazine.

[13]  S. Bramble.  Image analysis for the biological sciences , 1996 .

[14]  Christopher Jennison,et al.  A Subpixel Image Restoration Algorithm , 1997 .

[15]  William E. Higgins,et al.  Nonlinear filtering approach to 3-D gray-scale image interpolation , 1996, IEEE Trans. Medical Imaging.

[16]  Håvard Rue,et al.  A Loss Function Model for the Restoration of Grey Level Images , 1997 .

[17]  Martin Fleury,et al.  Sampling concerns in scanline algorithms , 1997, IEEE Transactions on Medical Imaging.

[18]  Michael Unser,et al.  Enlargement or reduction of digital images with minimum loss of information , 1995, IEEE Trans. Image Process..

[19]  Jayaram K. Udupa,et al.  Shape-based interpolation of multidimensional grey-level images , 1994, Medical Imaging.

[20]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[21]  Giovanni Ramponi,et al.  Warped distance for space-variant linear image interpolation , 1999, IEEE Trans. Image Process..