Minimum Variance Spatial Filtering Research Articles

Inverse Problem Analysis in Magnetic Nanoparticle Tomography Using Minimum Variance Spatial Filter

In magnetic nanoparticle tomography (MNT), the reduction of artifacts and the calculation time can be used to estimate the position of magnetic nanoparticles (MNPs). A non-negative least-squares (NNLS) inverse problem analysis has been used in MNT systems for this task. However, due to the presence of measurement noise and the high sensitivity of the NNLS method, it often estimates certain MNPs inaccurately, i.e., it generates artifacts. In addition, its calculation time is very high. In this study, we applied the minimum variance spatial filter (MV-SF) inverse problem analysis to MNT and estimated the position of an MNP sample containing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\mu \text{g}$ </tex-math></inline-formula> of Fe. Using the MV-SF method, MNP samples placed at a depth of 25–40 mm were observed to have no artifacts. Moreover, the MV-SF method was also observed to be faster than the NNLS method by a factor of approximately 20. These results verify the feasibility of the MV-SF method for estimating the MNP positions in an MNT system.

Magnetoencephalography with temporal spread imaging to visualize propagation of epileptic activity.

We describe temporal spread imaging (TSI) that can identify the spatiotemporal pattern of epileptic activity using Magnetoencephalography (MEG). A three-dimensional grid of voxels covering the brain is created. The array-gain minimum-variance spatial filter is applied to an interictal spike to estimate the magnitude of the source and the time (Ta) when the magnitude exceeds a predefined threshold at each voxel. This calculation is performed through all spikes. Each voxel has the mean Ta (<Ta>) and spike number (Nsp), which is the number of spikes whose source exceeds the threshold. Then, a random resampling method is used to determine the cutoff value of Nsp for the statistically reproducible pattern of the activity. Finally, all the voxels where the source exceeds the threshold reproducibly shown on the MRI with a color scale representing <Ta>. Four patients with intractable mesial temporal lobe epilepsy (MTLE) were analyzed. In three patients, the common pattern of the overlap between the propagation and the hypometabolism shown by fluorodeoxyglucose-positron emission tomography (FDG-PET) was identified. TSI can visualize statistically reproducible patterns of the temporal and spatial spread of epileptic activity. TSI can assess the statistical significance of the spatiotemporal pattern based on its reproducibility.

Linearly constrained minimum variance spatial filtering for localization of conductivity changes in electrical impedance tomography.

We localize dynamic electrical conductivity changes and reconstruct their time evolution introducing the spatial filtering technique to electrical impedance tomography (EIT). More precisely, we use the unit-noise-gain constrained variation of the distortionless-response linearly constrained minimum variance spatial filter. We address the effects of interference and the use of zero gain constraints. The approach is successfully tested in simulated and real tank phantoms. We compute the position error and resolution to compare the localization performance of the proposed method with the one-step Gauss-Newton reconstruction with Laplacian prior. We also study the effects of sensor position errors. Our results show that EIT spatial filtering is useful for localizing conductivity changes of relatively small size and for estimating their time-courses. Some potential dynamic EIT applications such as acute ischemic stroke detection and neuronal activity localization may benefit from the higher resolution of spatial filters as compared to conventional tomographic reconstruction algorithms.

Extracting Reverberant Sound Using a Linearly Constrained Minimum Variance Spatial Filter

Microphone arrays are typically used to extract the direct sound of sound sources while suppressing noise and reverberation. Applications such as immersive spatial sound reproduction commonly also require an estimate of the reverberant sound. A linearly constrained minimum variance filter, of which one of the constraints is related to the spatial coherence of the assumed reverberant sound field, is proposed to obtain an estimate of the sound pressure of the reverberant field. The proposed spatial filter provides an almost omnidirectional directivity pattern with spatial nulls for the directions-of-arrival of the direct sound. The filter is computationally efficient and outperforms existing methods.

Array-Gain Constraint Minimum-Norm Spatial Filter With Recursively Updated Gram Matrix For Biomagnetic Source Imaging

This paper proposes a novel spatial filter for biomagnetic source imaging. The proposed spatial filter is derived based on a modified version of the minimum-norm spatial filter and is designed to have a performance close to that of the adaptive minimum-variance spatial filter through the use of an estimated covariance matrix. In this method, the theoretical form of the measurement covariance matrix is estimated as an updated gram matrix in a recursive procedure. Since the proposed method does not use the sample covariance matrix, it is free of the well-known weaknesses of the minimum-variance spatial filter, namely, the proposed spatial filter does not require a large number of time samples, and it can even be applied to single-time-sample data. It is also robust to source correlation. We have validated the method's effectiveness by our computer simulations as well as through experiments using auditory-evoked magnetoencephalographic data.

Array-gain constraint minimum-norm spatial filter with recursively updated gram matrix for bioelectromagnetic source imaging

Event Abstract Back to Event Array-gain constraint minimum-norm spatial filter with recursively updated gram matrix for bioelectromagnetic source imaging Kensuke Sekihara1* and Isamu Kumihashi1 1 Tokyo Metropolitan University, Department of Systems Design and Engineering, Japan The spatial filter is a popular method used to reconstruct a source distribution from bioelectromagnetic data. When the weight of a spatial filter only depends on the geometry of the measurements, such a spatial filter is referred to as a non-adaptive spatial filter, which includes the well-known minimum-norm filter [1]. The weight of an adaptive spatial filter depends not only on the measurement geometry but also on the measurement covariance matrix. A representative adaptive spatial filter is the minimum-variance spatial filter [2]. Although adaptive spatial filters generally have performances better than non-adaptive spatial filters, adaptive spatial filters have well-known weaknesses. First, since the computation of their weights requires a sample covariance matrix of the measured data, a large number of time samples are needed to obtain an accurate sample covariance matrix. Second, the adaptive spatial filter is known to be sensitive to the source correlation, and it generally fails to reconstruct source activities when they are highly correlated. In this paper, we propose a novel spatial filter based on the array-gain constrained minimum-norm filter, which is a modified version of the minimum-norm filter. The proposed method is designed to estimate the theoretical form of the measurement covariance matrix through recursively updating the gram matrix. The method is able to provide three-dimensional volume reconstruction with a spatial resolution considerably higher than that of existing minimum-norm-based methods. Nonetheless, the method is free of the above-mentioned weaknesses occurring with adaptive spatial filters, because it does not use the sample covariance matrix. The method is also robust to the source correlation, and this robustness can be seen in our computer simulation as well as in our experiments using auditory-evoked MEG data.

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

This paper discusses the location bias and the spatial resolution in the reconstruction of a single dipole source by various spatial filtering techniques used for neuromagnetic imaging. We first analyze the location bias for several representative adaptive and non-adaptive spatial filters using their resolution kernels. This analysis theoretically validates previously reported empirical findings that standardized low-resolution electromagnetic tomography (sLORETA) has no location bias. We also find that the minimum-variance spatial filter does exhibit bias in the reconstructed location of a single source, but that this bias is eliminated by using the normalized lead field. We then focus on the comparison of sLORETA and the lead-field normalized minimum-variance spatial filter, and analyze the effect of noise on source location bias. We find that the signal-to-noise ratio (SNR) in the measurements determines whether the sLORETA reconstruction has source location bias, while the lead-field normalized minimum-variance spatial filter has no location bias even in the presence of noise. Finally, we compare the spatial resolution for sLORETA and the minimum-variance filter, and show that the minimum-variance filter attains much higher resolution than sLORETA does. The results of these analyses are validated by numerical experiments as well as by reconstructions based on two sets of evoked magnetic responses.