Improved image interpolation using bilateral filter for weighted least square estimation

New edge-directed interpolation (NEDI) consists two steps. The two steps are parameter and data estimation. The second step can be replaced by a recently proposed technique called soft-decision to consider the consistency of image structure during this data estimation. The original idea of both steps is to assume equal variances for all estimation errors, such that an ordinary least squares (OLS) estimator can be used. Due to the existence of noise, different object layers, changing in image structures, different spatial distance to the missing data, etc, we observe that the estimation errors of data samples have unequal variances. Hence, a weighted least square (WLS) estimator should be used for both steps. The bilateral filter, which can accurately remove noise and preserve image structure, has been used to model successfully the weights of squared residuals, such that we can apply it to both steps of the estimation. Experimental results show that the average PSNR of this improved interpolation method is 0.47 dB and 0.23 dB higher than two similar approaches, NEDI and Soft-decision Adaptive Interpolation (SAI) using 24 natural images from Kodak. The subjective results show improvement as well.