Influence of Unknown Exterior Samples on Interpolated Values for Band-Limited Images

The growing size of digital images and their increasing information content in terms of bits per pixel (or signal-to-noise ratio (SNR)) lead us to ask to what extent the known samples permit restoration of the underlying continuous image. In the context of band-limited data the Shannon--Whittaker theory gives an adequate theoretical answer provided that infinitely many samples are measured. Yet, we show that the current accuracy of digital images will be limited in the future by the truncation error. Indeed, with eight-bit images this error was small compared to other perturbations such as quantization or aliasing. With 16-bit images, it is no longer negligible. To do so, we propose a method to estimate the truncation error. All of our results are expressed in terms of root mean squared error (RMSE) under the common hypothesis of band-limited weakly stationary random processes. As a first contribution, we present a general expression of the truncation RMSE involving the spectral content of the image. We t...

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