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This paper proposes a novel method for the image interpolation problem based on two-dimensional discrete wavelet transform (DWT) with the edge preserving approach. The purpose of this method is to consider two contrasting issues of over-smoothing and creation of spurious edges at the same time, and offer a novel solution based on statistical dependencies of image sub-bands, and noise behavior. The offered method has a multi-faceted approach for the problem; by sub-band coding, it handles each 2D-DWT image sub-band with a different solution. For LH and HL sub-bands, two algorithms work together in order to preserve regularity. Area_Check algorithm is a four-phase edge-preserving algorithm that aims to recognize and interpolate separating lines of environments and edgy regions in the best possible way. On the other hand, RLS_AVG algorithm interpolates smooth surfaces of the image by keeping the regularity of the image without over-smoothing. In this regard, the offered algorithm has a great power to counter jaggies and annoying artifacts. In the end, in order to demonstrate the capability, and performance of the proposed method, the final results in various metrics are compared with the results of the most famous and the newest image interpolation methods. [ABSTRACT FROM AUTHOR]

This research presents a Bayesian nonparametric (BNP) clustering method for estimating filter-bank coefficients of discrete wavelet transform (DWT) for high-performance single-image super-resolution (SISR). The statistical model works on the idea of an “infinite mixture model” that operates using a Markov chain without a predefined number of states. Using the hierarchical dirichlet process (HDP) that uses blocked Gibbs Sampling to obtain the desired final values, the model extracts statistical dependencies between coarse and finer scales. Also, it defines a compound Poisson process (CPP) to model the DWT coefficients within a specific scale, granting the ability to perfectly predict, model, and remove the Poisson noise of the image at the same during the process. Thus, the proposed unsupervised HDP–CPP model observes and exploits statistical inter-scale and intra-scale dependencies of image sub-bands. Despite deep neural network-based SISR methods that require training of millions of weights in some cases, this approach provides a flexible and versatile platform with much less complexity and the ability to model the correlation of distant pixels. This method has excellent upscaling and denoising capabilities, and outperforms state-of-the-art methods with noticeably sharper images using a very small image-bank of less than 30 high-resolution and low-resolution images. [ABSTRACT FROM AUTHOR]