The Kalman filter is widely acknowledged as a linear optimal estimator. However, it is usually considered to have taxing computational and storage requirements in the field of image superresolution. This work presents an innovative Kalman filter–based method to solve the inherent problems of the Kalman filter and make it feasible for superresolution applications. Unlike other Kalman filter–based methods, we did not assume the pixels of high-resolution (HR) image are uncorrelated and the covariance matrix is diagonal for the calculation simplification. Instead, we take the spatial correlation of the pixels within a local block of HR image into consideration and propose a block diagonal assumption for the prediction covariance after a new construction way of the column vector which represents the HR image is presented. This significantly reduces the computational complexity during the Kalman filtering. Then, we develop a point-wise Kalman filter method to reduce the computational complexity and decrease the storage requirement. Furthermore, an iterative scheme is proposed to overcome the inaccurate initial estimation problem of superresolution reconstruction. The experiments with synthetic and real data show that the proposed method is effective and outperforms other superresolution methods.