Page 45 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue

ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1

MSICA: MULTI-SCALE SIGNAL DECOMPOSITION BASED ON INDEPENDENT
COMPONENT ANALYSIS WITH APPLICATION TO DENOISING AND
RELIABLE MULTI-CHANNEL TRANSMISSION

Abolfazl Hajisami and Dario Pompili
Dept. of Electrical and Computer Engineering, Rutgers University–New Brunswick, NJ, USA

Abstract – Multi-scale decomposition is a signal description method in which the signal is decomposed into multiple
scales, which has been shown to be a valuable method in information preservation. Much focus on multi-scale decom-
position has been based on scale-space theory and wavelet transform. In this article, a new powerful method to perform
multi-scale decomposition exploiting Independent Component Analysis (ICA), called MSICA, is proposed to translate
an original signal into multiple statistically independent scales. It is proven that extracting the independent components
of the even and odd samples of a digital signal results in the decomposition of the same into approximation and detail.
It is also proven that the whitening procedure in ICA is equivalent to a filter bank structure. Performance results of
MSICA in signal denoising are presented; also, the statistical independency of the approximation and detail is exploited
to propose a novel signal-denoising strategy for multi-channel noisy transmissions aimed at improving communication
reliability by exploiting channel diversity.

Keywords – Channel Diversity, Independent Component Analysis, Multi-scale Decomposition, Wavelet Transform.

1. INTRODUCTION passing the signal through a low-pass filter and high-

Overview: Multi-scale decomposition is an invaluable pass filter, respectively, followed by a downsampling by
a factor of 2. This results in a decomposition of the
tool in digital signal processing with applications such signal into different scales, which can be considered as
as those in [1, 2, 3, 4, 5], where an original signal is de- low and high frequency bands. Multi-scale decomposi-
composed into a set of signals, each of which provides tion by wavelet transforms has a number of advantages
information about the original signal at a different scale. over the scale-space decomposition and empirical mode
A major signal-processing task where multi-scale decom- decomposition [20]. First, since the signal information
position has been shown to be very useful is denoising, at one scale is not contained in another scale, signal in-
based on the intuition that information pertaining to the formation at different scales are better separated in the
noise would be accurately characterized in certain scales wavelet domain. Second, scale selection when perform-
that are separate from the scales of the signal. The ing noise suppression using wavelet decomposition is less
main literature works in multi-scale decomposition have critical than that for noise suppression using scale-space
focused on scale-space decomposition [6, 7, 8, 9, 10], decomposition as all the scales are considered in noise
empirical mode decomposition [11, 12, 13], and wavelet suppression using wavelet decomposition as opposed to a
transform [14, 15, 16, 17, 18]. single scale as done in scale-space decomposition. How-
In scale-space theory [19], a signal is decomposed into a ever, there are a number of limitations pertaining to
single-parameter family of signals with a progressive noise suppression using wavelet transform [20]. For in-
decrease in fine scale signal information between suc- stance, signals processed using wavelet transforms can
cessive scales. This allows analyzing signals at coarser exhibit oscillation artifacts related to wavelet basis func-
scales without the influence of finer scales such as those tions used in the wavelet transform, which is particularly
pertaining to noise. Knowing this, one can employ scale- noticeable in low Signal-to-Noise Ratio (SNR) regimes.
space theory to suppress noise by performing scale-space Moreover, in DWT the approximation and detail are
decomposition on the signal and then treating one of not statistically independent, which may cause a poor
signals at a coarser scale as the noise-suppressed sig- performance in signal denoising.
nal. However, selecting the scale that represents the
noise-suppressed signal can be challenging. Moreover, Motivation and Approach: Given these limitations
noise suppression using scale-space theory does not fa- of both space-scale and wavelet decomposition in terms
cilitate the fine-grained noise suppression at the individ- of signal denoising, we were motivated to explore al-
ual scales, which limits its overall flexibility in striking a ternative approaches. We investigate the problem of
balance between noise suppression and signal structural decomposing a signal into multiple scales from a differ-
preservation [20]. ent point of view, i.e., we propose a new approach that
In Discrete Wavelet Transform (DWT), the original sig- takes a statistical perspective on multi-scale decomposi-
nal is decomposed into approximation and detail by tion according to which a signal is considered as a mix-

© International Telecommunication Union, 2020 25