A Gradient-Regularized Deep Learning Method for Restoring Image in Myopic Vision

Mobile photography is often limited by complex, lens-specific optical aberrations. While recent deep learning methods approach this as an end-to-end deblurring task, these "black-box" models lack explicit optical modeling and can hallucinate details. Conversely, classical blind deconvolution remains highly unstable. To bridge this gap, we present Lens2Zernike, a deep learning framework that blindly recovers physical optical parameters from a single blurred image. To the best of our knowledge, no prior work has simultaneously integrated supervision across three distinct optical domains. We introduce a novel physics-consistent strategy that explicitly minimizes errors via direct Zernike coefficient regression (z), differentiable physics constraints encompassing both wavefront and point spread function derivations (p), and auxiliary multi-task spatial map predictions (m). Through an ablation study on a ResNet-18 backbone, we demonstrate that our full multi-task framework (z+p+m) yields a 35% improvement over coefficient-only baselines. Crucially, comparative analysis reveals that our approach outperforms two established deep learning methods from previous literature, achieving significantly lower regression errors. Ultimately, we demonstrate that these recovered physical parameters enable stable non-blind deconvolution, providing substantial in-domain improvement on the patented Institute for Digital Molecular Analytics and Science (IDMxS) Mobile Camera Lens Database for restoring diffraction-limited details from severely aberrated mobile captures.

Though there exists a reasonable forward model for blur based on optical physics, recovering depth from a collection of defocused images remains a computationally challenging optimization problem. In this paper, we show that with contemporary optimization methods and reasonable computing resources, a global optimization approach to depth from defocus is feasible. Our approach rests on alternating minimization. When holding the depth map fixed, the forward model is linear with respect to the all-in-focus image. When holding the all-in-focus image fixed, the depth at each pixel can be computed independently, enabling embarrassingly parallel computation. We show that alternating between convex optimization and parallel grid search can effectively solve the depth-from-defocus problem at higher resolutions than current deep learning methods. We demonstrate our approach on benchmark datasets with synthetic and real defocus blur and show promising results compared to prior approaches. Our code is available at github.com/hollyjackson/dfd.

We introduce ErA (Error-Aware Deep Unrolling Network), an end-to-end frame work for single-image defocus deblurring. ErA jointly learns a compact kerne basis and per-pixel weights, while an error-aware term in Augmented Lagrangian unrolling corrects kernel estimation errors via alternating updates and ResUNet denoisers. It achieves state-of-the-art PSNR/SSIM on DPDD, RealDOF, and RTF, and shows strong generalization on CUHK without ground truth.