Tarig Ballal

Maaz Mahadi, Tarig Ballal, Muhammad Moinuddin et al.

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned. This often occurs when the feature space's dimensionality is higher than or comparable to the training data size. Regularized LDA (RLDA) methods based on regularized linear estimators of the data covariance matrix have been proposed to cope with such a situation. The performance of RLDA methods is well studied, with optimal regularization schemes already proposed. In this paper, we investigate the capability of a positive semidefinite ridge-type estimator of the inverse covariance matrix that coincides with a nonlinear (NL) covariance matrix estimator. The estimator is derived by reformulating the score function of the optimal classifier utilizing linear estimation methods, which eventually results in the proposed NL-RLDA classifier. We derive asymptotic and consistent estimators of the proposed technique's misclassification rate under the assumptions of a double-asymptotic regime and multivariate Gaussian model for the classes. The consistent estimator, coupled with a one-dimensional grid search, is used to set the value of the regularization parameter required for the proposed NL-RLDA classifier. Performance evaluations based on both synthetic and real data demonstrate the effectiveness of the proposed classifier. The proposed technique outperforms state-of-art methods over multiple datasets. When compared to state-of-the-art methods across various datasets, the proposed technique exhibits superior performance.

Basit O. Alawode, Mudassir Masood, Tarig Ballal et al.

In spite of the improvements achieved by the several denoising algorithms over the years, many of them still fail at preserving the fine details of the image after denoising. This is as a result of the smooth-out effect they have on the images. Most neural network-based algorithms have achieved better quantitative performance than the classical denoising algorithms. However, they also suffer from qualitative (visual) performance as a result of the smooth-out effect. In this paper, we propose an algorithm to address this shortcoming. We propose a deep collaborative filtering-based (Deep-CoFiB) algorithm for image denoising. This algorithm performs collaborative denoising of image patches in the sparse domain using a set of optimized neural network models. This results in a fast algorithm that is able to excellently obtain a trade-off between noise removal and details preservation. Extensive experiments show that the DeepCoFiB performed quantitatively (in terms of PSNR and SSIM) and qualitatively (visually) better than many of the state-of-the-art denoising algorithms.

Alam Zaib, Tarig Ballal, Shahid Khattak et al.

Linear discriminant analysis (LDA) based classifiers tend to falter in many practical settings where the training data size is smaller than, or comparable to, the number of features. As a remedy, different regularized LDA (RLDA) methods have been proposed. These methods may still perform poorly depending on the size and quality of the available training data. In particular, the test data deviation from the training data model, for example, due to noise contamination, can cause severe performance degradation. Moreover, these methods commit further to the Gaussian assumption (upon which LDA is established) to tune their regularization parameters, which may compromise accuracy when dealing with real data. To address these issues, we propose a doubly regularized LDA classifier that we denote as R2LDA. In the proposed R2LDA approach, the RLDA score function is converted into an inner product of two vectors. By substituting the expressions of the regularized estimators of these vectors, we obtain the R2LDA score function that involves two regularization parameters. To set the values of these parameters, we adopt three existing regularization techniques; the constrained perturbation regularization approach (COPRA), the bounded perturbation regularization (BPR) algorithm, and the generalized cross-validation (GCV) method. These methods are used to tune the regularization parameters based on linear estimation models, with the sample covariance matrix's square root being the linear operator. Results obtained from both synthetic and real data demonstrate the consistency and effectiveness of the proposed R2LDA approach, especially in scenarios involving test data contaminated with noise that is not observed during the training phase.

Muzammil Behzad, Mudassir Masood, Tarig Ballal et al.

In this paper, we propose a novel image denoising algorithm using collaborative support-agnostic sparse reconstruction. An observed image is first divided into patches. Similarly structured patches are grouped together to be utilized for collaborative processing. In the proposed collaborative schemes, similar patches are assumed to share the same support taps. For sparse reconstruction, the likelihood of a tap being active in a patch is computed and refined through a collaboration process with other similar patches in the same group. This provides very good patch support estimation, hence enhancing the quality of image restoration. Performance comparisons with state-of-the-art algorithms, in terms of SSIM and PSNR, demonstrate the superiority of the proposed algorithm.