Multi-frame super-resolution image reconstruction aims to restore a highresolution image by fusing a set of low-resolution images. The low-resolution images are usually subject to some degradation, such as warping, blurring, down-sampling, or noising, which causes substantial information loss in the low-resolution images, especially in the texture regions. The missing information is not well estimated using existing traditional methods. In this paper, having analyzed the observation model describing the degradation process starting with a high-resolution image and moving to the low-resolution images, we propose a more reasonable observation model that integrates the missing information into the super-resolution reconstruction. Our approach is fully formulated in a Bayesian framework using the Kullback-Leibler divergence. In this way, the missing information is estimated simultaneously with the B Shengrong Zhao Circuits Syst Signal Process high-resolution image, motion parameters, and hyper-parameters. Our proposed estimation of the missing information improves the quality of the reconstructed image. Experimental results presented in this paper show improved performance compared with that of existing traditional methods.
The median-type filter is an effective technique to remove salt and pepper (SAP) noise; however, such a mechanism cannot always effectively remove noise and preserve details due to the local diversity singularity and local non-stationarity. In this paper, a two-step SAP removal method was proposed based on the analysis of the median-type filter errors. In the first step, a median-type filter was used to process the image corrupted by SAP noise. Then, in the second step, a novel-designed adaptive nonlocal bilateral filter is used to weaken the error of the median-type filter. By building histograms of median-type filter errors, we found that the error almost obeys Gaussian–Laplacian mixture distribution statistically. Following this, an improved bilateral filter was proposed to utilize the nonlocal feature and bilateral filter to weaken the median-type filter errors. In the proposed filter, (1) the nonlocal strategy is introduced to improve the bilateral filter, and the intensity similarity is measured between image patches instead pixels; (2) a novel norm based on half-quadratic estimation is used to measure the image patch- spatial proximity and intensity similarity, instead of fixed L1 and L2 norms; (3) besides, the scale parameters, which were used to control the behavior of the half-quadratic norm, were updated based on the local image feature. Experimental results showed that the proposed method performed better compared with the state-of-the-art methods.
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