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By Satoru Iwata, Satoko Moriguchi, Kazuo Murota

This paper offers a swifter set of rules for the M-convex submodular How challenge, that is a generalization of the minimum-cost How challenge with an M-convex fee functionality for the How-boundary, the place an M-convex functionality is a nonlinear nonseparable cliserete convex functionality on integer issues. The set of rules extends the skill sealing process lor the submodular How challenge via Fleischer. Iwata and MeCormiek (2002) using a singular means of altering the capability by way of fixing greatest submodular How difficulties.

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The MAPES-EM algorithms provide excellent spectral estimates with relatively minor artifacts. 1 (10 dB higher than in the previous experiments). 01, 77 (60%) missing samples] obtained via. (a) WFFT, (b) GAPES with M = 64 and = 10−2 , (c) MAPES-EM1 with M = 64 and = 10−3 , and (d) MAPES-EM2 with M = 64 and = 10−3 . corresponding moduli of the spectral estimates of complete-data WFFT, APES, missing-data WFFT, GAPES, MAPES-EM1, and MAPES-EM2 are plotted in Figs. 6(f ), respectively. Again, the performance of the MAPES-EM algorithms is excellent.

We can see that GAPES can still resolve the two vertical spectral lines clearly. 1 INTRODUCTION In this chapter, we review the APES algorithm for complete-data spectral estimation following the derivations in [13], which provide a “maximum likelihood (ML) fitting” interpretation of the APES estimator. They pave the ground for the missing-data algorithms we will present in later chapters. 2. The APES algorithm N−1 for any given frequency ω. 1) into L overlapping subvectors (data snapshots) of size M × 1 with the following shifted structure: y¯ l = [yl yl+1 · · · yl+M−1 ]T , l = 0, .

Through numerical simulations, we demonstrate the excellent performance of the MAPES algorithms for missing-data spectral estimation and missing-data restoration. 2, we give a brief review of the EM algorithm for the missing-data problem. 4, we develop two nonparametric MAPES algorithms for the missing-data spectral estimation problem via the EM algorithm. 5. 6, we compare MAPES with GAPES for the missing-data problem. 7 to illustrate the performance of the MAPES-EM algorithms. 2 EM FOR MISSING-DATA SPECTRAL ESTIMATION Assume that some arbitrary samples of the uniformly sampled data sequence N−1 are missing.

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