Supervisor: Dr. Ahmadiyan directed by: Seyed Behnam Mousavi Biomedical Engineering Department. January

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Biomedical Engineering Department. January 2018 Fig. 1 Examples of typical artefacts produced by the magnetic field gradients during six sequences used in this study (at 1.5 T): SSFP: steady-state free precession, SE: spin echo, SPGR: spoiled gradient recoiled, EPI: echo planar imaging, Diff: diffusion, FSE: fast spin echo 17

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Fig. 3 Workflow of the study presenting the acquisition of the ECG, the constitution and the use of the training and holdout sets 19

PRINCIPLE OF THE ADAPTIVE STEP SIZE LMS FILTER According to the LTI theory, the optimal value of μ can be computed with the following formula: var(gradients) is the maximum variance of the magnetic field gradients in the three directions G X, G Y and G Z. 20 Biomedical Engineering Department. January 2018

METHOD TO OBTAIN THE GOLD STANDARD ECG Decided to use the ideal solution of adaptive filtering the Wiener–Hopf It yields the best filtering the LMS or any other adaptive filters can achieve × because of its offline computation, it cannot be used in real time. 21 Biomedical Engineering Department. January 2018

METHOD TO OBTAIN THE GOLD STANDARD ECG CONTINUED.. 22 Biomedical Engineering Department. January 2018

Metric to assess the effect of LMS step size on ECG denoising quality: definition of E, ε, and μexp we defined the energy of the difference between the LMS-corrected ECG and the gold standard ECG during gradient emission, divided by the time of gradient emission : Then, the energy E was normalized to obtain a percentage ε(μ) using the formula: 23 Biomedical Engineering Department. January 2018

Fig. 5 Example of E(μ) curve for μ [5e −7 ; 7e −4 ]. The curve corresponds to acquisitions with SSFP sequence at 1.5 T within the training set. The minimum of the curve: min[E(μ)] defines the value μ exp 24 Biomedical Engineering Department. January 2018

Use of the training set to parameterize the adaptive and standard LMS filters Use of the holdout set to compare existing real ‑ time filters and the adaptive LMS: 1. Filtering with the adaptive LMS. 2. Filtering with a standard LMS using the fixed step size optimized within the training set: μ standard. 3. Filtering with a LMS using a fixed step size optimized for each sequence: μ exp [11]. 4. Filtering with a Kalman filter optimized for each database [9]. 5. Filtering with a standard low-pass filter [1, 2] with a cutoff frequency of 13 Hz. 6. No filtering. 25 Biomedical Engineering Department. January 2018

TWO DIFFERENT TESTS WERE PERFORMED: 1. The LMS filters performances were assessed in term of noise reduction using the parameter ε previously defined 2. The six filtering methods (adaptive LMS, fixed LMS, optimized LMS, optimized Kalman filter, low pass filter, and no filtering) were assessed in terms of QRS detection performance. cumulative error (CE) index, defined by: 26 Biomedical Engineering Department. January 2018

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