Empirical Mode Decomposition

Empirical Mode Decomposition And Fractal Dimension Filter A Novel Technique for Denoising Explosive Lung Sounds Anovel technique for denoising explosive lung S o u n d s ( E L S s ) , s u c h a s f i n e / c o a r s e c r a c k l es a n d squawks (SQs), is presented here. A combination of emp ir i ca l m ode d ecom pos iti on (E MD ) and f r a cta l dimension (FD) analysis is proposed to form a denoising EMD-FD filter. The latter decomposes the data into a number of intrinsic mode functions and automatically selects their important and unimportant portions, which lead to the estimation of the denoised ELS signal and the background noise, respectively. Experimental results prove efficient performance of the EMD-FD filter (mean delectability 98.4%; sensitivity 98.1%; specificity 97.7%) in sustainin g both time location and structural characteristics of ELS. Lung sounds facilitate the noninvasive diagnosis of pulmonary diseases, since the acoustic energy generated by breathing is highly associated with the relevant pulmonary dysfunction [11],[2]. One of the major issues that attracts attention in the field of lun g sound research is the accurate detection Of lung sounds, such as ELSs. This is due to the non stationary nature of' ELSs given that they behave as transient signals of a short time duration superimposed on the underlying vesicular sound. The most common types of ELSs are crackles and SQs [1], [2], with crackles being further categorized to fine crackles (FCs) and coarse crackles (CCs), according to their time and frequency-domain features [3], [4]. In particular, FCs are exclusively inspiratory high-pitched events met in mid to late inspiration with repetitive, patternlike behavior over subsequent breaths [5]. They are primarily initiated by explosive reopening of small airways that had closed during the previous expiration [5]. Unlike FCs, CCs are both inspiratory and expiratory events with a frequency content lower than that of FCs, and they tend to be less reproducible across subsequent breaths [5]. Their production mechanism is considered to be the existence of fluid in small airways; thus, CCs can change pattern or clear after cou ghing. FCs are heard in congestive heart failure or pulmonary fibrotic disease (asbestosis and idiopathic fibrosis [1]), while CCs are related to chronic bronchitis [I]. SQs area combination of FCs and wheezes I 11, similar to a short wheeze initiated with an FC. They are produced by explosive reopening and fluttering of the unstable airway, which causes the short wheeze [5] and are associated with allergic alveolitis and interstitial fibrosis [51.

Many research efforts in extracting ELS from the remaining vesicular sound, which is defined as background noise in this study, have shown promise, especially when involving advanced signal processing methodolo g ies, such as hi g her-order statistics, neuro-fuzzy modelin g , wavelet transform (WT), and FD. Comparative result ,,, of these approaches can be found in 161. Recently, a combination of wT with FD has been proposed, amalgamating the advantages of both methodologies and forming a ll efficient denoisin g tool, namely WT-FD filter [7], [8]. In this article, the combinatory approach followed in the WT-FD filter is extended to the field of EMD [9]. Instead of WT, the EMD is employed to decompose the sound signal into components with well-defined instantaneous frequency. Each characteristic oscillatory mode extracted, namely intrinsic mode function _(IMF), is symmetric and has a unique local frequency, and different IMFs do not exhibit the same frequency at the same time [9]. In this way, the oscillatory characteristics of ELS are reflected to the IMFs analysis domain. Consequently, by applyin g FD analysis in the latter, the important (hi g h FD value) and unimportant (low I'D value) portions of IMFs can be identified, corresponding to ELSs and background noise, respectively. Since none of the signal is lost in the EMD procedure, the sum of the selected portions of IMFs per category gives back the denoised ELSs and the background noise, accordingly. The aforementioned approach forms a new denoising tool, namely EMD-FD filter, which adaptively capture the non stationary aspect of ELSs and successfully extracts them from the background noise, as demonstrated from experimental results drawn from the EMD-FD-based analysis of' real lung sound recordings. This makes the EMD-FD filter applicable to similar separation problems involving nonstationary transient signals mixed with uncorrelated background noise, which is considered wide-sense stationary within consistent segments. Methods EMD The oscillatory behavior of lung sound recordin gs is analyzed using EMD [9]. The EMD method is necessary to deal with

Fig. 1. Characteristics and a working excmple of the proposed approach. (a) A schematic representation of the noniterative structure of the EMD-FD filter. (b) Original data (Signal x(t) with arrowheads pointing out the signal of interest (ELS), eleven intrinsic modes (c j(t), I = 1,2….11 )) and the residue r 11 (t). (c) The estimated ηx,λ=1,2…..11,parameter corresponding to the eleven, intrinsic modes of (b), from where the value of L = 3 is -deduced according_to (2). (d) A working example of the production procedure of the binary thresholds SBTH 1(t) and NBTH1(t) (see steps A3 and A4), derived from the first intrinsic mode C1 (t). both nonstationary and nonlinear data and, contrary to almost all the previous methods, EMD is intuitive, i.e., the basis of the expansion is generated in a direct, a posteriori, and adaptive way, derived from the data [9]. The main idea behind EMD is that all data consist of different simple intrinsic modes of oscillations, represented by the IMFs. An IMF represents a simple oscillatory mode as a counterpart of the simple harmonic function, yet it allows amplitude and frequency modulation; thus, it is much more general. According to Huang et al. [9], an IMF satisfies two conditions:  in the whole dataset, the number of extrema and the number of zero-crossings must either be equal or differ at most by one at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero. The EMD method considers the signals at their local oscillation scale, subtract the faster oscillation, and iterates theresidual. In particular, by virtue of the IMF definition, the EMD procedure for a given signal x(t) can be summarized as follows [9]: 1) Identify the successive extrema of x(t) based on the sign alterations across the derivative of x(t). 1) Extract the upper and lower envelopes by interpolation, i.e., the local maxima (minima) are connected by a cubic spline interpolation to produce the upper (lower) envelope; these envelopes should cover all the data between them. 2) Compute the average of upper and lower envelopes, nil (t). 3) Calculate the first component h, (t) = x(t) - m I (t). 2) Ideally, h, (t) should be an IMF. In reality, however, overshoots and undershoots are common, which also generate new extrema and shift or exaggerate the existing ones (9]. To correct this, the shifting process has to be repeated as many times as is required to reduce the extracted signal as an IMF. To this end, treat h 1 (t) as a new set of data, and repeat steps 1-4 up to k times (e.g., k= 7) until h 1 k (t) becomes a true IMF. Then set e 1 (t) = h 1 k (t). Overall, c 1 (t) should contain the finest scale or the shortest period component of the signal. 6) Obtain the residue rj (t)- x(t) - cl (t). 7) Treat r i (t) as a new set of data and repeat steps 1- 6 up to N times until the residue r N (t) becomes a constant, a monotonic function, or a function with only one cycle from which no more IMFs can he extracted. Note that even for data with zero mean, rN(t) still can differ from zero.

8)

Finally N

x(t )   ci (t )  rN (t ) i 1

where ci(t ) is the ith IMF and rN(t) the final residue. The above procedure results in a decomposition of the data into N-empirical nodes and a residue r N (t), which can be either a monotonic function or a single cycle. It is noteworthy that, in order to apply the EML` method, there is no need for a mean or zero reference; EMD only needs the locations of the local extrema to generate the zero reference for each component (except for the residue) through the shifting process. A useful characteristic of (I) is the potential of filtering that it provides. Indeed, using the IMF components, a time-space filtering can be devised simply by selecting a specific range of them in the reconstruction procedure [e.g., in (1), for high-pass filtering: i = I : k, k < N or for bandpass one: b : k, I < 1), k < N]. This time-space filtering has the filtering advantage that its results preserve the full nonlinearity and nonstationary property in the physical space 1101. FD Analysis Although the ability of time-space filtering offered by (1) seems to provide a solution to the denoising of ELS, it is not Sufficient on its own. In fact, even when a number of IMFs are excluded from the reconstruction procedure, due to their strong correlation with the noise, some noise terms still exist within the remaining IMFs, which mainly correlate with the ELS. A solution to this problem may be deduced from an FD-based analysis [7], [8], [11]. This is due to the property of FD to provide a relative measure of the number of basic building