How to take advantage of aliasing in bandlimited signals
In signal processing systems, aliasing is normally treated as a disturbing signal. That motivates the need for effective analog, optical and digital anti-aliasing filters. However, aliasing also conveys valuable information on the signal above the Nyquist frequency. Hence, an effective processing of the samples, based on a model of the input signal, would virtually allow the sampling frequency to be increased using slower and cheaper converters. We present such an algorithm for bandlimited signals that are sampled below twice the maximum signal frequency. Using a subspace method in the frequency domain, we show that these signals can be reconstructed from multiple sets of samples. The offset between the sets is unknown and can have arbitrary values. This approach can be applied to the creation of super-resolution images from sets of low resolution images. In this application, registration parameters have to be computed from aliased images. We show that parameters and high resolution images can be computed precisely, even when high levels of aliasing are present on the low resolution images.