We discuss a few new motion deblurring problems that are significant to kernel estimation and non-blind deconvolution. We found that strong edges do not always profit kernel estimation, but instead under certain circumstance degrade it. This finding leads to a new metric to measure the usefulness of image edges in motion deblurring and a gradient selection process to mitigate their possible adverse effect. We also propose an efficient and high-quality kernel estimation method based on using the spatial prior and the iterative support detection (ISD) kernel refinement, which avoids hard threshold of the kernel elements to enforce sparsity. We employ the TV-ℓ
deconvolution model, solved with a new variable substitution scheme to robustly suppress noise.