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Image classification forms an important class of problems in machine learning and is widely used in many realworld applications, such as medicine, ecology, astronomy, and defense. Convolutional neural networks (CNNs) are machine learning techniques designed for inputs with grid structures, e.g., images, whose features are spatially correlated. As such, CNNs have been demonstrated to be highly effective approaches for many image classification problems and have consistently outperformed other approaches in many image classification and object detection competitions. A particular challenge involved in using machine learning for classifying images is measurement data loss in the form of missing pixels, which occurs in settings where scene occlusions are present or where the photodetectors in the imaging system are partially damaged. In such cases, the performance of CNN models tends to deteriorate or becomes unreliable even when the perturbations to the input image are small. In this work, we investigate techniques for improving the performance of CNN models for image classification with missing data. In particular, we explore training on a variety of data alterations that mimic data loss for producing more robust classifiers. By optimizing the categorical cross-entropy loss function, we demonstrate through numerical experiments on the MNIST dataset that training with these synthetic alterations can enhance the classification accuracy of our CNN models.