Preserving original noise residuals in images are critical to image fraud identification. Since the resizing operation during deep learning will damage the microstructures of image noise residuals, we propose a framework for directly training images of original input scales without resizing. Our arbitrary-sized image training method mainly depends on the pseudo-batch gradient descent (PBGD), which bridges the gap between the input batch and the update batch to assure that model updates can normally run for arbitrary-sized images. In addition, a 3-phase alternate training strategy is designed to learn optimal residual kernels for image fraud identification. With the learnt residual kernels and PBGD, the proposed framework achieved the state-of-the-art results in image fraud identification, especially for images with small tampered regions or unseen images with different tampering distributions.