Shift selection influence in partial cycle spinning denoising of biomedical signals

Abstract

Denoising of biomedical signals using wavelet transform is a widely used technique. The use of undecimated wavelet transform (UWT) assures better denoising results but implies a higher complexity than discrete wavelet transform (DWT). Some implementation schemes have been proposed to perform UWT, one of them is Cycle Spinning (CS). CS is performed using the DWT of several circular shifted versions of the signal to analyse. The reduction of the number of shifted versions of the biomedical signal during denoising process used is addressed in the present work. This paper is about a variant of CS with a reduced number of shifts, called Partial Cycle Spinning (PCS), applied to ultrasonic trace denoising. The influence of the choice of PCS shifts in the denoised registers quality is studied. Several shifts selection rules are proposed, compared and evaluated. Denoising results over a set of ultrasonic registers are provided for PCS with different shift selection rules, CS and DWT. The work shows that PCS with the appropriate choice of shifts could be the best option to denoise biomedical ultrasonic traces.

Reduced Cycle Spinning Method for the Undecimated Wavelet Transform

“…If all the possible shifts are performed, M=K, the number of operations would be approximately 4CK2. Different methods based on the selection of a limited number of shifts have been proposed to reduce the order of the CS operations from O(K2) to O(Klog2(K)) [10,17,19]. The proposed RCS method eliminates all iDWTs except one, reducing the operations in the synthesis from 2CKM to 2CK.…”

“…Therefore, the RCS method reduces the number of operations from 4CKM to 2CK(M+1), very close to the half value. In addition, the RCS method can be combined with other approximated CS methods as the ones proposed in References [10,17,19] increasing the computational cost reduction.…”

“…An alternative to reduce the number of shifts M=2J is the PCS method. The PCS method introduced in References [17,18,19] is an approximation of the CS method with a reduced number of shifts, M<2J. The PCS method selects a subset of the shifts and performs the UWT in a similar way to the CS method.…”

“…The CS method has been used in the processing of different kinds of images: astronomical images [10], synthetic aperture radar images [11], medical images for diagnosis [12] and for estimation of fluid flows [13], or the classic image of Lena [14]. However, CS has been also used for the extraction of signal characteristics from electrical discharges [15], for denoising in electromagnetic signals from geophysical explorations [16] or for denoising of ultrasonic signals used both for nondestructive evaluations [17,18] and for medical diagnosis [19,20].…”

“…These periodicities allowed the proposal of some alternatives to reduce the computational cost in the CS method. One of them was the Partial Cycling Spinning (PCS) method [17,19] that performs the CS method using only a subset of the circular shifted versions of the signal to process, reducing the number of DWTs and iDWTs.…”