Faezeh Yeganli

Image super-resolution via sparse representation over multiple learned dictionaries based on edge sharpness

A new algorithm for single-image super-resolution based on selective sparse representation over a set of coupled dictionary pairs is proposed. Patch sharpness measure for high- and low-resolution patch pairs defined via the magnitude of the gradient operator is shown to be approximately invariant to the patch resolution. This measure is employed in the training stage for clustering the training patch pairs and in the reconstruction stage for model selection. For each cluster, a pair of low- and high-resolution dictionaries is learned. In the reconstruction stage, the sharpness measure of a low-resolution patch is used to select the cluster it belongs to. The sparse coding coefficients of the patch over the selected low-resolution cluster dictionary are calculated. The underlying high-resolution patch is reconstructed by multiplying the high-resolution cluster dictionary with the calculated coefficients. The performance of the proposed algorithm is tested over a set of natural images. PSNR and SSIM results show that the proposed algorithm is competitive with the state-of-the-art super-resolution algorithms. In particular, it significantly out-performs the state-of-the-art algorithms for images with sharp edges and corners. Visual comparison results also support the quantitative results.

Image super-resolution via sparse representation over multiple learned dictionaries based on edge sharpness and gradient phase angle

This paper introduces an algorithm for single-image super-resolution based on selective sparse representation over a set of low- and high-resolution cluster dictionary pairs. Patch clustering in the dictionary training stage and model selection in the reconstruction stage are based on patch sharpness and orientation defined via the magnitude and phase of the gradient operator. For each cluster, a pair of coupled low- and high- resolution dictionaries is learned. In the reconstruction stage, the most appropriate dictionary pair is selected for the low- resolution patch and the sparse coding coefficients with respect to the low- resolution dictionary are calculated. A high-resolution patch estimate is obtained by multiplying the sparse coding coefficients with the corresponding high-resolution dictionary. The performance of the proposed algorithm is tested over a set of natural images. Results validated in terms of PSNR, SSIM and visual comparison indicate that the proposed algorithm is competitive with the state-of-the-art super-resolution algorithms.

Selective super-resolution via sparse representations of sharp image patches using multiple dictionaries and bicubic interpolation

This paper proposes an extension to the algorithm of single-image super-resolution based on selective sparse representation over a set of coupled low and high resolution dictionary pairs. The extended algorithm reserves the sparse representation framework for patches of high sharpness values while bicubic interpolation is used to super-resolve un-sharp patches. A set of cluster dictionary pairs is used for the super-resolution process. If a patch belong to a low sharpness cluster, it is super-resolved using bicubic interpolation. Otherwise, the this patch is sparsely coded over the clusters low resolution dictionary. Then, the sparse coding coefficients of the low resolution patch along with the clusters high resolution patch are used to estimate the corresponding high resolution patch. It is found empirically that a large percentage of patches have low sharpness values. Therefore, the usage of bicubic interpolation significantly reduces the super-resolution computational complexity, without sacrificing the reconstruction quality. Experimental results conducted over several images validate this result in terms of the PSNR and SSIM measures.

Improved online dictionary learning for sparse signal representation

In this paper a new dictionary learning algorithm is proposed. Similar to many dictionary learning algorithms, the proposed algorithm alternates between two stages. First, sparse coding stage uses the current dictionary to obtain the sparse representation coefficients. Herein, the orthogonal matching pursuit algorithm is used for sparse coding. Second, a dictionary update stage that employs the calculated coefficients to update the dictionary and is based on iterative least squares method. The autocorrelation and the cross correlation between the sparse coding coefficients and the training data are estimated recursively by applying a forgetting factor. The variable step size which depends on the forgetting factor and autocorrelation function is derived. The simulation results indicate that representation ability of dictionaries designed by the proposed method has improved SNR compared to those designed with existing state of the art algorithms with faster convergence. Preliminary results for single image super-resolution are promising.

Image Super-Resolution via Sparse Representation over Coupled Dictionary Learning Based on Patch Sharpness

In this paper a new algorithm for single-image super-resolution based on sparse representation over a set of coupled low and high resolution dictionary pairs is proposed. The sharpness measure is defined via the magnitude of the gradient operator and is shown to be approximately scale-invariant for low and high resolution patch pairs. It is employed for clustering low and high resolution patches in the training stage and for model selection in the reconstruction stage. A pair of low and high resolution dictionaries is learned for each cluster. The sharpness measure of a low resolution patch is used to select the appropriate cluster dictionary pair for reconstructing the high resolution counterpart. The sparse representation coefficients of low and high resolution patches are assumed to be equal. By multiplying the high resolution dictionary and the sparse coding coefficient of a low resolution patch, the corresponding high resolution patch is reconstructed. Simulation results in terms of PSNR and SSIM and visual comparison, indicate the superior performance of the proposed algorithm compared to the leading super-resolution algorithms in the literature over a set of natural images in sharp edges and corners.

Improved dictionary learning by constrained re-training over residual components

The dictionary learning process aims at training for a dictionary that can loyally and sparsely represent data in a given training set. In this paper, we propose performing a second pass of dictionary learning where the training set is composed of the residuals of the original training set as calculated with respect to the outcome of a first pass of dictionary learning. In the second pass, the dictionary is updated with the residual signals. However, the representation fidelity of the original training set is imposed. This is formulated as a constrained optimization problem and is solved using Lagrange multipliers with a line-search. The proposed strategy is shown to train dictionaries with better representation capabilities compared to dictionaries trained with standard dictionary learning. This result is validated with tests concluded over the problem of image representation.

Super-resolution using multiple structured dictionaries based on the gradient operator and bicubic interpolation

In this paper we present an extension to the algorithm of super-resolution via selective sparse representation over a set of coupled low and high resolution cluster dictionary pairs. Patch clustering and sparse model selection are carried out using the magnitude and phase of the patch gradient operator. A compact dictionary pair is learned for each cluster. A low resolution patch is classified into one of the clusters using the two criteria. A high resolution patch is reconstructed using the high resolution cluster dictionary, and the spare representation coefficients of its low resolution counterpart over the low resolution cluster dictionary. This extension aims at super-resolving patches of low sharpness or poor directionality with bicubic interpolation. Accordingly, the computationally expensive sparse representation framework will only be applied on a limited portion of image patches. As a result, the super-resolution reconstruction computational complexity is significantly reduced without sacrificing the performance. Experiments conducted over natural images validate this result.

A Strategy for Residual Component-Based Multiple Structured Dictionary Learning

A new strategy for multiple structured dictionary learning is proposed. It is motivated by the fact that a signal and its residual after sparse approximation do not necessarily possess the same geometric structure. Based on the geometric structure of each residual component, the most appropriate dictionary is selected. A single-atom sparse representation vector of this residual is calculated and the chosen dictionary is updated. For a given training signal, the process of model (dictionary) selection and one-atom representation is repeated until the desired sparsity or approximation error is reached. Thus, the proposed strategy provides a mechanism whereby each signal can update the most relevant dictionaries based on the structure of its residuals. Simulations conducted over natural images show that, in comparison to standard single or multiple dictionary learning and sparse representation approaches, the proposed strategy significantly improves the representation quality.

Single Image Super-Resolution via Sparse Representation over Directionally Structured Dictionaries Based on the Patch Gradient Phase Angle

We propose a single-image super-resolution algorithm based on sparse representation over a set of cluster dictionary pairs. For each cluster, a directionally structured dictionary pair is designed. The dominant angle in the patch gradient phase matrix is employed as an approximately scale-invariant measure. This measure serves for patch clustering and sparse model selection. The dominant phase angle of each low resolution patch is found and used to identify its corresponding cluster. Then, the sparse coding coefficients of this patch with respect to the low resolution cluster dictionary are calculated. These coefficients are imposed on the high resolution dictionary of the same cluster to obtain a high resolution patch estimate. In experiments conducted on several images, the proposed algorithm is shown to out-perform the algorithm that uses a single universal dictionary pair, and to be competitive to the state-of-the art algorithm. This is validated in terms of PSNR, SSIM and visual comparison.