Image preprocessing is an important process during pattern recognition which increases the recognition performance. Linear convolution filtering is a primary preprocessing method used to enhance particular local patterns of the image which are essential for recognizing the images. However, because of the vast search space of the preprocessing filter, almost no earlier studies have tackled the problem of identifying an optimal preprocessing filter that yields effective features for input images. This paper proposes a novel design method for the optimal preprocessing filter corresponding to a given task. Our method calculates local image bases of the training dataset and represents the optimal filter as a linear combination of these local image bases with the optimized coefficients to maximize the expected generalization performance. Thereby, the optimization problem of the preprocessing filter is converted to a lower-dimensional optimization problem. Our proposed method combined with a higher-order local auto-correlation (HLAC) feature extraction exhibited the best performance both in the anomaly detection task with the conventional pattern recognition algorithm and in the classification task using the deep convolutional neural network compared with typical preprocessing filters.