A fast computation method for time scale signal denoising

Abstract

This paper presents a novel and fast scheme for signal denoising in the wavelet domain. It exploits the time scale structure of the wavelet coefficients by modeling them as superposition of simple atoms, whose spreading in the time scale plane formally is the solution of a couple of differential equations. In this paper, we will show how the numerical solution of such equations can be avoided leading to a speed up of the scale linking computation. This result is achieved through a suitable projection space of the wavelet local extrema, requiring just least squares and filtering operations. Intensive experimental results show the competitive performances of the proposed approach in terms of signal to noise ratio (SNR), visual quality and computing time.

Time-Scale Similarities for Robust Image De-noising

“…The wavelet transform w(u, s) of a function f can be approximated through a linear combination of predefined atoms [34] as follows…”

“…Nonethe- Table 1 512 × 512 × 8 bits Lena, Barbara, Peppers and Boats images. Comparisons (PSNR) between ANL-means and the denoising approaches in [5,6,12,13,28,31,32,34] less, the similarity measure in (10) gives it the second dimension, since it is able to detect edges as connected curves composed of neighboring and similar time-scale atoms. An example is shown in Fig.…”

“…], while α h,s = α h s γ h −1 . The equality in (15) can be derived if each basic atom F (t k , u, s) is written as the wavelet transform of ramp signals, whose equation is r k (t) = (t − t k )χ [t k ,+∞] -see [34] for details.…”

“…The algorithm works on rows and columns respectively of the vertical and horizontal sub-bands of image 2D Wavelet Transform (2D-WT) [34], that is a redundant transform. In fact, the atomic approximation is not robust to decimation since it can cause the loss of extremum points from a dyadic scale to another and the change of atoms shape.…”

“…Wavelet time-scale representation has been adopted in this paper due to its ability in characterizing the regularity of edge points through the decay of the amplitude of the corresponding wavelet coefficients along scales [14,33]. In particular, the properties of the atomic approximation in [34] are very appropriate for the final task. The latter approximates wavelet details through interacting atoms (i.e.…”