Fractal dimension estimation and noise filtering using Hough transform

This paper considers the scenario of a periodic signal consisting of a sum of sinusoids with different unknown frequencies and phases superimposed on fractal noise of an unknown fractal dimension. A novel method is reported to estimate the fractal dimension of the noise. The problem is first converted to a line detection problem. Then the Hough transform is applied. A comparison with the least-squares estimation method is reported. It is shown that the method detects the fractal dimension more accurately and robustly. Using the estimated fractal dimension, the Wiener filter is used to remove the fractal noise. Its performance is also compared with some other common filters. Finally, an indicator is suggested to estimate the likelihood that the input signal belongs to the desired signal model, i.e. a periodic signal with superimposed fractal noise. © 2004 Elsevier B.V. All rights reserved.