De-Hankelization of singular spectrum analysis matrices via an optimization approach for blood glucose estimation

For the conventional diagonal averaging method, it computes the average of the elements in each shifted diagonal of each two dimensional singular spectrum analysis matrix to obtain each element in each one dimensional singular spectrum analysis vector. However, this conventional diagonal averaging method does not guarantee to obtain the optimal singular spectrum analysis vectors. To address this issue, this paper proposes an optimization approach for performing the de-Hankelization process in the singular spectrum analysis. In particular, each singular spectrum analysis vector is optimized such that the two norm difference between each two dimensional singular spectrum analysis matrix and each corresponding Hankel matrix generated by each one dimensional singular spectrum analysis vector is minimized subject to its infinity norm constraint. This problem is actually a standard quadratic programming problem and an existing interior point method is applied for finding its solution. The obtained singular spectrum analysis vectors are applied to estimate the blood glucose level.