Modification in the SAR Super-Resolution Model Using the Fractal Descriptor LMME in the Term Regularizer

Abstract

This paper presents a modified simultaneous auto regressive (SAR) super-resolution model, by adding a fractal operator as a new regularized term. We propose the local morphologic multifractal exponent (LMME) descriptor to determine the hyperparameters estimation of the probability distribution function representing the high resolution (HR) image. Due to the LMME’s texture sensibility characteristic, the estimated HR images showed good enhancements in their edge elements and detail regions when compared with the images generated by the original SAR model, at the same time that mitigates the unwanted noise. The proposed modification was also extended to the model that combines the SAR method with $\ell _{1}$ -norm. A comparison using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) metrics is presented in order to measure the quality of the HR images estimated by the proposed methods in relation to other available. The use of the LMME descriptor presented better adjustments of the restored image estimation distributions parameters, reflected on the values of PSNR and SSIM obtained in the experiments using low resolution images with moderate noise levels (SNR of 30 dB and 40 dB). In addition, our proposal converges in fewer iterations.