Dr. Rizwan Khalid
brings ill-posed images
back into focus.

Dr. Rizwan Khalid specializes in image deblurring, numerical analysis, scientific computing, and machine learning. His doctoral research at the Abdus Salam School of Mathematical Sciences focused on developing advanced preconditioning techniques to improve Krylov subspace methods for solving large-scale nonlinear systems arising from mean-curvature-based image deblurring models.

His work introduced and analyzed efficient block preconditioners with strong spectral properties, including clustered, real, and positive eigenvalues that support faster and more reliable convergence. He also developed computationally efficient algorithms that exploit diagonal dominance, symmetric positive definiteness, and translation invariance to reduce processing costs. A major contribution of his research was the development of an advanced restrictively preconditioned BiCGSTAB method and the novel (P_R) preconditioner, which demonstrated superior performance compared with existing approaches.

Extensive numerical experiments confirmed improved convergence, reduced computational complexity, and enhanced image restoration quality, as measured through Peak Signal-to-Noise Ratio (PSNR). His doctoral work provides a strong theoretical and practical contribution to solving complex inverse problems in image processing with high accuracy and computational efficiency.

Currently, his research focuses on integrating neural networks with sparse systems to develop intelligent and efficient methods for solving large-scale scientific and computational problems.