This paper presents a two-phase kernel estimation method for robust motion deblurring. The authors address the challenge of kernel estimation in motion deblurring, where strong edges can degrade performance. They propose a new metric to measure the usefulness of image edges and a gradient selection process to mitigate their adverse effects. The method uses a spatial prior and iterative support detection (ISD) kernel refinement to achieve efficient and high-quality kernel estimation without enforcing hard thresholds on kernel elements. A TV-ℓ₁ deconvolution model is employed, solved with a new variable substitution scheme to robustly suppress noise. The two-phase method first estimates a coarse kernel without enforcing sparsity, then refines it using ISD to enforce sparsity adaptively. The first phase uses Gaussian priors and multi-scale processing to efficiently estimate the kernel. The second phase employs ISD to iteratively detect support regions and refine the kernel, ensuring sparsity and preserving large-value elements. The method also introduces a spatial prior to preserve sharp edges during latent image restoration. The TV-ℓ₁ deconvolution model is used to restore the latent image, with an efficient solver based on half-quadratic splitting. The method is tested on challenging examples with large PSFs due to camera shake, showing improved performance compared to existing methods. The results demonstrate that the method effectively handles small structures and noise, producing high-quality deblurred images. The method is efficient, with the two-phase kernel estimation being computationally feasible, and is shown to work well on both synthetic and real-world images. The authors conclude that their method provides a robust and efficient solution for motion deblurring, particularly in scenarios with strong and narrow structures.This paper presents a two-phase kernel estimation method for robust motion deblurring. The authors address the challenge of kernel estimation in motion deblurring, where strong edges can degrade performance. They propose a new metric to measure the usefulness of image edges and a gradient selection process to mitigate their adverse effects. The method uses a spatial prior and iterative support detection (ISD) kernel refinement to achieve efficient and high-quality kernel estimation without enforcing hard thresholds on kernel elements. A TV-ℓ₁ deconvolution model is employed, solved with a new variable substitution scheme to robustly suppress noise. The two-phase method first estimates a coarse kernel without enforcing sparsity, then refines it using ISD to enforce sparsity adaptively. The first phase uses Gaussian priors and multi-scale processing to efficiently estimate the kernel. The second phase employs ISD to iteratively detect support regions and refine the kernel, ensuring sparsity and preserving large-value elements. The method also introduces a spatial prior to preserve sharp edges during latent image restoration. The TV-ℓ₁ deconvolution model is used to restore the latent image, with an efficient solver based on half-quadratic splitting. The method is tested on challenging examples with large PSFs due to camera shake, showing improved performance compared to existing methods. The results demonstrate that the method effectively handles small structures and noise, producing high-quality deblurred images. The method is efficient, with the two-phase kernel estimation being computationally feasible, and is shown to work well on both synthetic and real-world images. The authors conclude that their method provides a robust and efficient solution for motion deblurring, particularly in scenarios with strong and narrow structures.