We implement the popular Adaptive weights Conjugate gradient Toeplitz (ACT) algorithm for signal construction. This algorithm is fast and accurate, and we show its effectiveness in several typical trace regularization situations. This algorithm requires an estimate of the bandwidth as input, and overestimating the bandwidth can cause spurious high frequency noise in the reconstruction. As an improvement, we implement a modified version of ACT that is less well known Multi-level ACT performs automatic bandwidth detection on its input by performing ACT iteratively to estimate the optimum reconstruction bandwidth. We test this algorithm on a harmonic of unknown bandwidth, and results show that Multi-level ACT is effective when the signal bandwidth can not be accurately estimated. A toolbox has been assembled that can be requested from the authors.
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