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FIGURE 4. Spectrum of the noise free PPG signal (average of two PPG channels) along with acceleration data (X, Y, and Z-axis data) are shown (Case 1). The spectrum of the PPG and the accelerometer data are in different scales. The red circle marker indicates the actual HR (in BPM) for that frame. Here it is evident that the effect of MA is not significant in the recorded PPG signal and hence it is possible to estimate HR without any denoising operation.

Figure 4 Spectrum of the noise free PPG signal (average of two PPG channels) along with acceleration data (X, Y, and Z-axis data) are shown (Case 1). The spectrum of the PPG and the accelerometer data are in different scales. The red circle marker indicates the actual HR (in BPM) for that frame. Here it is evident that the effect of MA is not significant in the recorded PPG signal and hence it is possible to estimate HR without any denoising operation.

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FIGURE 1. a. Dominant frequencies, fn (denoted by green dots) extracted from accelerometer data are illustrated along with actual heart rate (ground truth) for a single subject (Subject 7). b. Distributions of the most dominant components (MDC) and the second most dominant components (SMDC) are presented in the box plot to visualize the variation among the dominant frequency components in different subjects. c. The distribution of the lower frequency components (LFC) and the higher frequency components (HFC) are depicted which ensures that two separable frequency components exist in most of the accelerometer frames during physical exercise.
FIGURE 1. a. Dominant frequencies, fn (denoted by green dots) extracted from accelerometer data are illustrated along with actual heart rate (ground truth) for a single subject (Subject 7). b. Distributions of the most dominant components (MDC) and the second most dominant components (SMDC) are presented in the box plot to visualize the variation among the dominant frequency components in different subjects. c. The distribution of the lower frequency components (LFC) and the higher frequency components (HFC) are depicted which ensures that two separable frequency components exist in most of the accelerometer frames during physical exercise.
FIGURE 2. Proposed algorithm for HR estimation. Noise corrupted frames are selected and then the proposed DERMANC scheme is employed to estimate the candidate frequencies. Finally, a verification and tracking technique is utilized for the accurate estimation of HR.
FIGURE 2. Proposed algorithm for HR estimation. Noise corrupted frames are selected and then the proposed DERMANC scheme is employed to estimate the candidate frequencies. Finally, a verification and tracking technique is utilized for the accurate estimation of HR.
FIGURE 3. Effect of averaging of two channel PPG data shown in spectral domain. Four different cases are considered in four rows depending on the location of original HR (marked by a red circle) on the spectral plot. First row (a-c) corresponds to the Case / where 1° channel with a misleading peak and second row (d-f) corresponds to the Case // where 24 channel with a misleading peak. Case /I/ ( both channels with misleading peak) and Case /V (both channels with correct peaks) are depicted in third (g-i) and fourth (j-l) row respectively. The red marker indicates the actual HR (in BPM) for that frame.
FIGURE 3. Effect of averaging of two channel PPG data shown in spectral domain. Four different cases are considered in four rows depending on the location of original HR (marked by a red circle) on the spectral plot. First row (a-c) corresponds to the Case / where 1° channel with a misleading peak and second row (d-f) corresponds to the Case // where 24 channel with a misleading peak. Case /I/ ( both channels with misleading peak) and Case /V (both channels with correct peaks) are depicted in third (g-i) and fourth (j-l) row respectively. The red marker indicates the actual HR (in BPM) for that frame.
FIGURE 5. Spectrum of the noise corrupted PPG signal (average of two PPG channels) along with acceleration data (X, Y, and Z-axis data) are illustrated (Case II). The spectrum of the PPG and the accelerometer data are in different scales. The red marker indicates the actual HR (in BPM) for that frame. Here the influence of the MA is clearly visible in the spectrum of the PPG signal.
FIGURE 5. Spectrum of the noise corrupted PPG signal (average of two PPG channels) along with acceleration data (X, Y, and Z-axis data) are illustrated (Case II). The spectrum of the PPG and the accelerometer data are in different scales. The red marker indicates the actual HR (in BPM) for that frame. Here the influence of the MA is clearly visible in the spectrum of the PPG signal.
FIGURE 7. Proposed DERMANC scheme. For three channels accelerometer data, we propose 3 separate operating blocks placed serially (ie. Block-X, Block-Y and Block-Z). A sample operation in a block is shown in the right side. Two components obtained by decomposing corresponding acc. data (using EMD or VMD) are used as reference to LMS-based ANC scheme.
FIGURE 7. Proposed DERMANC scheme. For three channels accelerometer data, we propose 3 separate operating blocks placed serially (ie. Block-X, Block-Y and Block-Z). A sample operation in a block is shown in the right side. Two components obtained by decomposing corresponding acc. data (using EMD or VMD) are used as reference to LMS-based ANC scheme.
FIGURE 8. Decomposition of a single channel of acceleration data using EMD. Time domain representation of the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are illustrated through (a)-(c). On the other hand, frequency spectrum corresponding to the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are depicted (d)-(f). For a better understanding, the whole DERMANC algo- rithm is demonstrated through a block diagram in Fig. 7. At first, the accelerometer data from three channels (x,y,z), labeled as x;(n), y;(n) and z;(n) respectively, are decomposed into several modes which Tepresents the potential noise components ui (n), uy, () and ut, (2), where/ = 1,2,...... D, number of modes and i denotes the frame index. Decomposi- tion of accelerometer data using EMD and VMD is depicted in Fig. 8 and Fig. 9, respectively. The prior analysis of noise reveals that the noise signals have only a few dominant peaks within the range of HR frequencies (around 60-180 BPM) and in most of the time number of dominant frequencies is found two, as shown in Fig. 1. Thus the first two modes obtained via VMD or EMD within heart rate range are used for MA removal. In Fig. 7, the candidate PPG signal frame d(n) is used as the signal input to Block-X while the first mode of decomposed X-ch (x;(1)) accelerometer, labeled as ul, (n), is used as the reference input to the first LMS filter. On the right side of Fig. 7, the Block-X is shown in an enlarged view. It can be observed that the input d[n] passes through two LMS blocks where first two modes of proposed decomposed acceleration signal are used as reference sequentially. The output of the first LMS filter of Block-X is then passed to the next LMS filter as input and the second mode of the x;(n), labeled as ui, (n) as reference input. The output of the Block-X, namely e,,,,(”) is then fed to Block-Y. Similar to the operations of Block-X, here two filters are used. The successive two stages of LMS filters utilize the two modes ui, (n) and ui, (n) derived from the decomposition operation over Y-axis accelerometer data sequentially as references. Thereafter, output of Block-Y, ey,,,(m) is passed to Block-Z where the modes Ur, (n) and ur, (n) from Z-axis accelerometer data are used as references. It is found at each block that, use of two LMS filters tries to reduce the effect of noise components corresponding to decomposed accelerometer data of a particular channel. As a result, the DERMANC For a better understanding, the whole DERMANC algo-
FIGURE 8. Decomposition of a single channel of acceleration data using EMD. Time domain representation of the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are illustrated through (a)-(c). On the other hand, frequency spectrum corresponding to the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are depicted (d)-(f). For a better understanding, the whole DERMANC algo- rithm is demonstrated through a block diagram in Fig. 7. At first, the accelerometer data from three channels (x,y,z), labeled as x;(n), y;(n) and z;(n) respectively, are decomposed into several modes which Tepresents the potential noise components ui (n), uy, () and ut, (2), where/ = 1,2,...... D, number of modes and i denotes the frame index. Decomposi- tion of accelerometer data using EMD and VMD is depicted in Fig. 8 and Fig. 9, respectively. The prior analysis of noise reveals that the noise signals have only a few dominant peaks within the range of HR frequencies (around 60-180 BPM) and in most of the time number of dominant frequencies is found two, as shown in Fig. 1. Thus the first two modes obtained via VMD or EMD within heart rate range are used for MA removal. In Fig. 7, the candidate PPG signal frame d(n) is used as the signal input to Block-X while the first mode of decomposed X-ch (x;(1)) accelerometer, labeled as ul, (n), is used as the reference input to the first LMS filter. On the right side of Fig. 7, the Block-X is shown in an enlarged view. It can be observed that the input d[n] passes through two LMS blocks where first two modes of proposed decomposed acceleration signal are used as reference sequentially. The output of the first LMS filter of Block-X is then passed to the next LMS filter as input and the second mode of the x;(n), labeled as ui, (n) as reference input. The output of the Block-X, namely e,,,,(”) is then fed to Block-Y. Similar to the operations of Block-X, here two filters are used. The successive two stages of LMS filters utilize the two modes ui, (n) and ui, (n) derived from the decomposition operation over Y-axis accelerometer data sequentially as references. Thereafter, output of Block-Y, ey,,,(m) is passed to Block-Z where the modes Ur, (n) and ur, (n) from Z-axis accelerometer data are used as references. It is found at each block that, use of two LMS filters tries to reduce the effect of noise components corresponding to decomposed accelerometer data of a particular channel. As a result, the DERMANC For a better understanding, the whole DERMANC algo-
FIGURE 9. Decomposition of a single channel of acceleration data using VMD. Time domain representation of the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are illustrated through (a)-(c). On the other hand, frequency spectrum corresponding to the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are depicted (d)-(f). scheme enhances the performance of the traditional ANC scheme significantly using decomposed mode as reference instead of directly using acceleration data, which has been explored in the Results and Analysis section analytically. As mentioned earlier, the proposed DERMANC scheme satisfactorily removes the MA-related modes from recorded PPG signals when the MA-related peaks appear far away from the previous estimation. But in the case of a close MA mode, the ANC scheme is performed in order to suppress MA softly instead of completely eliminating it. Hence, there is the possibility that an MA-related peak may still exist in the denoised PPG signal. In order to overcome this problem, we propose an algorithm where the priority of a peak does not merely depend on its amplitude in the PPG spectrum. Rather priority of different peaks is sorted again when any of the peaks is found close to any MA-related components f;,, where k = 1,2,....,6. In Algorithm 1, the proposed technique is demonstrated logically.
FIGURE 9. Decomposition of a single channel of acceleration data using VMD. Time domain representation of the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are illustrated through (a)-(c). On the other hand, frequency spectrum corresponding to the X-axis accelerometer data, decomposed mode 1, and mode 2, respectively are depicted (d)-(f). scheme enhances the performance of the traditional ANC scheme significantly using decomposed mode as reference instead of directly using acceleration data, which has been explored in the Results and Analysis section analytically. As mentioned earlier, the proposed DERMANC scheme satisfactorily removes the MA-related modes from recorded PPG signals when the MA-related peaks appear far away from the previous estimation. But in the case of a close MA mode, the ANC scheme is performed in order to suppress MA softly instead of completely eliminating it. Hence, there is the possibility that an MA-related peak may still exist in the denoised PPG signal. In order to overcome this problem, we propose an algorithm where the priority of a peak does not merely depend on its amplitude in the PPG spectrum. Rather priority of different peaks is sorted again when any of the peaks is found close to any MA-related components f;,, where k = 1,2,....,6. In Algorithm 1, the proposed technique is demonstrated logically.
Algorithm 1: Algorithm for Peak Priority Resolve
Algorithm 1: Algorithm for Peak Priority Resolve
Case I (ANC): Using an average of 3-channel accelerome- er data as a reference signal to ANC (LMS algorithm). TABLE 2. Comparison among different approaches in terms of performance measures considering all 12 subjects.
Case I (ANC): Using an average of 3-channel accelerome- er data as a reference signal to ANC (LMS algorithm). TABLE 2. Comparison among different approaches in terms of performance measures considering all 12 subjects.
TABLE 1. AAE and AAEP for all 12 subjects using proposed E-DERMANC and proposed V-DERMANC methods.
TABLE 1. AAE and AAEP for all 12 subjects using proposed E-DERMANC and proposed V-DERMANC methods.
FIGURE 11. The performances of independent soft, moderate or hard denoising schemes are compared with the proposed 3-level denoising scheme in the V-DERMANC algorithm. Here it is evident that the combined scheme offers the best result in terms of average absolute error (AAE).
FIGURE 11. The performances of independent soft, moderate or hard denoising schemes are compared with the proposed 3-level denoising scheme in the V-DERMANC algorithm. Here it is evident that the combined scheme offers the best result in terms of average absolute error (AAE).
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