Image blurs are a major source of degradation in an imaging system. There are various blur types, such as motion blur and defocus blur, which reduce image quality significantly. Therefore, it is essential to develop methods for recovering approximated latent images from blurry ones to increase the performance of the imaging system. In this paper, an image blur removal technique based on sparse optimization is proposed. Most existing methods use different image priors to estimate the blur kernel but are unable to fully exploit local image information. The proposed method adopts an image prior based on nonzero measurement in the image gradient domain and introduces an analytical solution, which converges quickly without additional searching iterations during the optimization. First, a blur kernel is accurately estimated from a single input image with an alternating scheme and a half-quadratic optimization algorithm. Subsequently, the latent sharp image is revealed by a non-blind deconvolution algorithm with the hyper-Laplacian distribution-based priors. Additionally, we analyze and discuss its solutions for different prior parameters. According to the tests we conducted, our method outperforms similar methods and could be suitable for dealing with image blurs in real-life applications.