Mahmoud Nazzal

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 single image super-resolution using sparsity and structured dictionary learning in wavelet domain

This paper introduces a single-image superresolution approach which is based on sparse representation over dictionaries learned in the wavelet domain. The diagonal detail subband learning and reconstruction is improved by designing two diagonal dictionaries; one for the diagonal and another for the anti-diagonal orientations. Four pairs (low resolution and high resolution) of subband dictionaries are designed. The sparse representation coefficients for the respective low and high resolution images are assumed to be the same. The proposed algorithm is compared with the leading super-resolution techniques and is shown to excel both visually and quantitatively, with an average PSNR raise of 0.82 dB over the Kodak set. Moreover, this algorithm is shown to significantly reduce the dictionary learning computational complexity by designing compactly sized structural dictionaries.

Single image super resolution based on sparse representation via directionally structured dictionaries

This paper introduces a single-image super-resolution algorithm based on selective sparse coding over several directionally structured learned dictionaries. The sparse coding of high-resolution (HR) image patch over a HR dictionary is assumed to be identical to that of the corresponding low-resolution (LR) patches as coded over a coupled LR dictionary. However, the training patches are clustered by measuring the similarity between a patch and a number of directional templates sets. Each template set characterizes directional variations possessing a specific directional structure. For each cluster, a pair of directionally structured dictionaries is learned; one dictionary for each resolution level. An analogous clustering is performed in the reconstruction phase; each LR image patch is decided to belong to a specific cluster based on its directional structure. This decision allows for selective sparse coding of image patches, with improved representation quality and reduced computational complexity [1]. With appropriate sparse model selection, the proposed algorithm is shown to out-perform a leading super-resolution algorithm which uses a pair of universal dictionaries. Simulations validate this result both visually and quantitatively, with an average of 0.2 dB improvement in PSNR over Kodak set and some benchmark images.

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.

Image demosaicing by an improved alternating projections algorithm based on dual-tree complex wavelet transform

Most digital cameras acquire image information as an incomplete down-sampled representation of the three basic color components, such that one color value is sampled per pixel location. Image demosaicing is the process of retrieving the missing two color components in each pixel. Demosaicing by alternating projections (AP) is one of the most successful demosaicing approaches. The contribution of this paper is developing enhancements to the existing AP algorithm by proposing the dual tree complex wavelet transform as a framework for the algorithm, strengthened with wavelet-based denoising to achieve better color channel reconstruction. The proposed enhancements result in an average 0.27 dB PSNR improvement as tested over the Kodak Photo CD set. Visual experimentations also verify this PSNR raise. The enhanced AP algorithm is also shown to perform comparably to the leading demosaicing techniques.

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.

Directionally-structured dictionary learning and sparse representation based on subspace projections

This paper presents a new strategy for directionally-structured dictionary learning and component-wise sparse representation. The signal space is divided into directional subspace triplets. Directionally-selective projection operators are designed for this purpose. Each triplet contains two orthogonal subspaces along with a remainder one. For each triplet, a compact dictionary is learned. Sparse representation is done in an analogous manner. The most-fitting dictionary triplet is selected for each signal based on its directional structure. Using the designed projection operators, the signal is decomposed into three subspace components living in the three triplet subspaces. The signals sparse approximation is obtained as the direct summation of the sparse approximations of these three components, each coded over its subspace dictionary. Experiments conducted over a set of natural images show that the proposed strategy improves the sparse representation coding quality over standard methods, as tested in the problem of image representation.