Selecting the Corner in the-Curve Approach to Tikhonov

Abstract—The performance of two methods for selecting the corner in the-curve approach to Tikhonov regularization is evaluated via computer simulation. These methods are selecting the corner as the point of maximum curvature in the-curve, and selecting it as the point where the product of abcissa and ordinate is a minimum. It is shown that both these methods resulted in significantly better regularization parameters than that obtained with an often-used empirical Composite REsidual and Smoothing Operator approach, particularly in conditions where corre-lated geometry noise exceeds Gaussian measurement noise. It is also shown that the regularization parameter that results with the minimum-product method is identical to that selected with another empirical zero-crossing approach proposed earlier. Index Terms—Electrocardiography, electroencephalography, inverse problems,-curve, regularization. I