Binary images are prevalent in digital systems and have a wide range of applications including texts, fingerprint recognition, handwritten signatures, stellar astronomy, barcodes, and vehicle license plates. The recorded binary images are often degraded by blur and additive noise due to environmental effects and imperfections in the imaging system. In this paper, we study the problem of recovering the sharp binary image and the blur kernel from the motion degraded observation. We propose a new minimization model by using the binary prior of image pixel and the $l_0$ norm of image gradient to enforce the estimated image to be binary and the image gradient to be sparse respectively. An effective numerical optimization algorithm is applied for solving the proposed model. Extensive experiments for blind binary image deconvolution demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM).

二进制图像在数字系统中很普遍，并且具有广泛的应用，包括文本，指纹识别，手写签名，恒星天文学，条形码和车辆牌照。由于环境影响和成像系统中的缺陷，记录的二进制图像通常会因模糊和附加噪声而降级。在本文中，我们研究了从运动退化的观察中恢复清晰的二值图像和模糊核的问题。我们通过使用图像像素的二进制先验和${升}_0$规范图像梯度以分别将估计图像强制为二值图像和稀疏图像梯度。一种有效的数值优化算法被应用于求解所提出的模型。盲二值图像反卷积的大量实验表明，该方法在视觉质量，峰值信噪比（PSNR）和结构相似性指数（SSIM）方面优于某些现有的最新方法。