Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural framework for incorporating dynamic EEG generation models in source localization. Here, a recently developed inverse solution is introduced, which uses spatiotemporal Kalman filtering tuned through likelihood maximization. Standard diagnostic tests for objectively evaluating Kalman filter performance are then described and applied to inverse solutions for simulated and clinical EEG data. These tests, employed for the first time in Kalman-filter-based source localization, check the statistical properties of the innovation and validate the use of likelihood maximization for filter tuning. However, this analysis also reveals that the filter's existing space- and time-invariant process model, which contains a single fixed-frequency resonance, is unable to completely model the complex spatiotemporal dynamics of EEG data. This finding indicates that the algorithm could be improved by allowing the process model parameters to vary in space.
In this study, the authors propose a novel technique for medical image watermark detection using the concept of the fractional differentiator (FD). The feature of FD as a non‐linear high‐pass filter helps in watermark detection. In the region of non‐interest, the watermark image has been added in a mid‐band frequency range of the discrete cosine transform coefficients of 8×8 different blocks by generating direct spread spectrum sequence. Their scheme produces noise‐free watermarked medical images. Furthermore, they derive the test statistics of the proposed detector, which is characterised by the fractional order q. The average errors in pixels (PEs), peak‐signal‐to‐noise ratio (PSNR), structural similarity index (SSIM) and cross‐correlation coefficient (CC) have been used to quantify the capability of the proposed technique over some state‐of‐the‐art techniques. The proposed technique shows that at a particular value of fractional order q, there is a significant reduction in average PEs. It causes an increment in PSNR, SSIM and CC. The proposed technique is tested on a large number of medical images and it is found that their proposed technique works better or comparable with other state‐of‐the‐art techniques.
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