The paper presents a novel two-phase kernel estimation method for robust motion deblurring. The authors observe that strong edges can degrade kernel estimation under certain conditions, leading to a new metric to measure the usefulness of image edges and a gradient selection process to mitigate their adverse effects. The method includes: 1. **Two-Phase Kernel Estimation**: - **Phase One**: Efficient kernel initialization using Gaussian priors and a multi-scale setting. - **Phase Two**: Kernel refinement using the Iterative Support Detection (ISD) algorithm, which adaptively enforces sparsity and preserves large-value elements. 2. **Fast Kernel Estimation**: - Utilizes a spatial prior to guide the recovery of a coarse version of the latent image, allowing for sharp recovery even with Gaussian regularizers. 3. **ISD-Based Kernel Refinement**: - Solves the problem of obtaining sparse PSFs by iteratively securing large-value elements, ensuring deblurring quality while removing noise. 4. **Fast TV-ℓ1 Deconvolution**: - Proposes a robust deconvolution model using a TV-ℓ1 objective function, solved with an efficient alternating minimization method based on half-quadratic splitting. The method is evaluated on challenging examples with large blur kernels, demonstrating its effectiveness in deblurring images with high-quality results. The authors also provide a detailed analysis of the impact of image structure on kernel estimation and propose a new criterion for selecting informative edges.The paper presents a novel two-phase kernel estimation method for robust motion deblurring. The authors observe that strong edges can degrade kernel estimation under certain conditions, leading to a new metric to measure the usefulness of image edges and a gradient selection process to mitigate their adverse effects. The method includes: 1. **Two-Phase Kernel Estimation**: - **Phase One**: Efficient kernel initialization using Gaussian priors and a multi-scale setting. - **Phase Two**: Kernel refinement using the Iterative Support Detection (ISD) algorithm, which adaptively enforces sparsity and preserves large-value elements. 2. **Fast Kernel Estimation**: - Utilizes a spatial prior to guide the recovery of a coarse version of the latent image, allowing for sharp recovery even with Gaussian regularizers. 3. **ISD-Based Kernel Refinement**: - Solves the problem of obtaining sparse PSFs by iteratively securing large-value elements, ensuring deblurring quality while removing noise. 4. **Fast TV-ℓ1 Deconvolution**: - Proposes a robust deconvolution model using a TV-ℓ1 objective function, solved with an efficient alternating minimization method based on half-quadratic splitting. The method is evaluated on challenging examples with large blur kernels, demonstrating its effectiveness in deblurring images with high-quality results. The authors also provide a detailed analysis of the impact of image structure on kernel estimation and propose a new criterion for selecting informative edges.