Reject outliers from a 1D signal based on a sliding window and a deviation threshold.

reject_outliers.py

def reject_outliers(arr, window_size, threshold):
    """
    Given a 1D signal, replace outliers with the average of the surrounding points.

    Does the following for every point:
        1. Computes the median of the sliding window
        2. Computes the percentage difference between the current point and the
           sliding window median
        3. If that deviation exceeds the given threshold, replaces that point with
           the average of the surrounding two points.
        4. Otherwise, returns the same point.

    Parameters
    ----------
    arr : 1D array
        Signal with outliers
    window_size : int
        Size of sliding window
    threshold : float
        Minimum acceptable percentage deviation (as decimal)
        
    Returns
    -------
    result : 1D array
        Original signal with outliers removed.
    """
    if len(arr.shape) > 1:
        print('Only 1D arrays supported.')
        return
    
    result = np.empty_like(arr)
    
    for i in range(0, arr.shape[0]):
        min_i = int(max(0, np.floor(i - window_size / 2)))
        max_i = int(min(arr.shape[0], np.floor(i + window_size / 2 + 1)))
        med = np.median(arr[min_i:max_i])
        dev = np.abs(arr[i] - med) / med
        if dev > threshold:
            result[i] = np.average([arr[i-1], arr[i+1]])
        else:
            result[i] = arr[i]
            
    return result