High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.

Novel Iterative Truncated Total Least Squares Algorithm for Image Restoration

Image restoration is a typical ill-posed inverse problem, which can be solved by a successful total least squares (TLS) method when not only the observation but the system matrix is also contaminated by addition noise. Considering the image restoration is a large-scale problem in general, project the TLS problem onto a subspace defined by a Lanczos bidiagonalization algorithm, and then the Truncated TLS method is applied on the subspace. Therefore, a novel iterative TTLS method, involving appropriate the choice of truncation parameter, is proposed. Finally, an Image reconstruction example is given to illustrate the effectiveness and robustness of proposed algorithm.

Reply to “Comments on ‘Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications’”*

The commenters confirm the errors identified and discussed in Smerdon et al., which either invalidated or required the reinterpretation of quantitative results from pseudoproxy experiments presented or used in several earlier papers. These errors have a strong influence on the spatial skill assessments of climate field reconstructions (CFRs), despite their small impacts on skill statistics averaged over the Northern Hemisphere. On the basis of spatial performance and contrary to the claim by the commenters, the Regularized Expectation Maximization method using truncated total least squares (RegEM-TTLS) cannot be considered a preferred CFR technique. Moreover, distinctions between CFR methods in the context of the discussion in the original paper are immaterial. Continued investigations using accurately described and faithfully executed pseudoproxy experiments are critical for further evaluation and improvement of CFR methods.

Comments on “Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications”

Smerdon et al. report two errors in the climate model grid data used in previous pseudoproxy-based climate reconstruction experiments that do not impact the main conclusions of those works. The errors did not occur in subsequent works and therefore have no impact on the results presented therein. Results presented here for the Climate System Model (CSM) using multiple pseudoproxy noise realizations show that the quantitative differences between the incorrect and corrected results are within the expected variability of the noise realizations. It should also be made clear that the climate reconstruction method used in Smerdon et al. to illustrate the nature of the errors, the Regularized Expectation Maximization method with Ridge Regression (RegEM-Ridge), is known to produce climate reconstructions with considerable variance loss and has been superseded by RegEM-TTLS (TTLS indicates truncated total least squares).