Adaptive Sparse Detector for Suppressing Powerline Component in EEG Measurements

Powerline interference (PLI) is a major source of interference in the acquisition of electroencephalogram (EEG) signal. Digital notch filters (DNFs) have been widely used to remove the PLI such that actual features, which are weak in energy and strongly connected to brain states, can be extracted explicitly. However, DNFs are mathematically implemented via discrete Fourier analysis, the problem of overlapping between spectral counterparts of PLI and those of EEG features is inevitable. In spite of their effectiveness, DNFs usually cause distortions on the extracted EEG features, which may lead to incorrect diagnostic results. To address this problem, we investigate an adaptive sparse detector for reducing PLI. This novel approach is proposed based on sparse representation inspired by self-adaptive machine learning. In the coding phase, an overcomplete dictionary, which consists of redundant harmonic waves with equally spaced frequencies, is employed to represent the corrupted EEG signal. A strategy based on the split augmented Lagrangian shrinkage algorithm is employed to optimize the associated representation coefficients. It is verified that spectral components related to PLI are compressed into a narrow area in the frequency domain, thus reducing overlapping with features of interest. In the decoding phase, eliminating of coefficients within the narrow band area can remove the PLI from the reconstructed signal. The sparsity of the signal in the dictionary domain is determined by the redundancy factor. A selection criteria of the redundancy factor is suggested via numerical simulations. Experiments have shown the proposed approach can ensure less distortions on actual EEG features.

Cation order in the crystal structure of ‘minasgeraisite-(Y)’

The crystal structure of ‘minasgeraisite-(Y)’, triclinic P1, a = 9.994(4), b = 7.705(3), c = 4.764(2) Å, α = 90.042(9), β = 90.218(14), γ = 90.034(9) (°), V = 366.8(5) Å3 and Z = 1, has been refined to an R1 index of 2.86% for 4170 observed (|Fo| > 4σF) reflections. Significant observed (|Fo| > 40–60 σF) reflections violate the presence of a 21-screw axis and an a-glide plane, negating the space group P21/a previously found for minerals of the gadolinite–datolite group. Averaging of the X-ray data in Laue groups 2/m and $\bar 1$ gives the following agreement indices: 2/m (9.68%) and $\bar 1$ (5.68%). The internal agreement index from averaging of identical reflections collected at multiple positions along the diffraction vector is significantly lower than that for the Laue group $\bar 1$: Rpsi = 2.40%, where 13,109 reflections were collected, 4288 are unique for P1 symmetry, and Rpsi is based on a mean data redundancy factor of > 3. Both the data merging and an |E2–1| value of 0.773 indicate that P1 is the correct space group. The general formula for the gadolinite–datolite group is W2XZ2T2O8V2 (Z = 2) which we have expanded to 20 anions (Z = 1) to show the W-site cation ordering present in ‘minasgeraisite-(Y)’. Bismuth, Ca and REE are ordered over four W sites, with Bi dominant at W1, Ca dominant at W2, and Y dominant at W3 and W4. The dominant constituent at the X sites is a vacancy, and Ca does not occur at the X sites. Significant B and Si are assigned to the Be-dominant Z sites, and the T sites are occupied by Si. The simplified ‘minasgeraisite-(Y)’ formula (Z = 1) is BiCa(Y,Ln)2(□,Mn)2(Be,B,Si)4Si4O16 [(OH),O]4. ‘Minasgeraisite-(Y)’ should be assigned to a triclinic subgroup of the gadolinite–datolite group, and its lower symmetry suggests that Ca-substituted gadolinites and hingganites should be examined for evidence of triclinic symmetry associated with cation order at the W sites.