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Abstract:
We propose a novel probabilistic method for detection of signals and reconstruction
of images in the presence of random noise. The method uses results from percolation
and random graph theories (see Grimmett (1999)). We address the problem of
detection and estimation of signals in situations where the signal-to-noise ratio is
particularly low.
We present an algorithm that allows to detect objects of various shapes in
noisy images. The algorithm has linear complexity and exponential accuracy. Our
algorithm substantially diers from wavelets-based algorithms (see Arias-Castro
et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate
of an object based on the noisy picture. This algorithm also has linear complexity
and is appropriate for real-time systems. We prove results on consistency and algorithmic
complexity of our procedures.
