Bayesian Image Interpolation Based on the Learning and Estimation of Higher Bandwavelet Coefficients

This paper presents an image interpolation algorithm based on the estimation of higher band wavelet coefficients. We presume that a given image is the LL band of the wavelet coefficients of a high resolution image that does not actually exist and is target of the interpolation. The proposed method estimates the higher band coefficients by learning the correlation of coefficients across the scale. According to the wavelet theory, a sequence of wavelet coefficients has extreme at the point that corresponds to the singularity of signal, and the extremes across the wavelet scale have some relationship. The main point of the wavelet domain interpolation is to exploit these properties of wavelet coefficients for estimating the extreme points in the higher frequency bands. In this paper, the relationship between the wavelet coefficients across the scale is described by Markov stochastic model, and each wavelet coefficient is modeled by Gaussian mixture that has multiple means and variances. For the enhanced subjective quality of interpolated image through the above modeling, we added refinement process using maximum a posteriori (MAP) technique. Comparison with the existing wavelet-domain and edge-preserving interpolation algorithms shows that the proposed method provides improved objective and subjective quality.