We consider the problem of restoring a noisy blurred image using an adaptive unsharp mask filter. Starting with a set of very high quality images, we use models for both the blur and the noise to generate a set of degraded images. With these image pairs, we optimally train the strength parameter of the unsharp mask to smooth flat areas of the image and to sharpen areas with detail. We characterize the blur and the noise for a specific hybrid analog/digital imaging system in which the original image is captured on film with a low-cost analog camera. A silver-halide print is made from this negative; and this is scanned to obtain a digital image. Our experimental results for this imaging system demonstrate the superiority of our optimal unsharp mask compared to a conventional unsharp mask with fixed strength.