| 1. |
- Behjat, Hamid, et al.
(author)
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Anatomically-adapted Graph Wavelets for Improved Group-level fMRI Activation Mapping
- 2015
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In: NeuroImage. - : Elsevier BV. - 1095-9572 .- 1053-8119. ; 123:Online 07 June 2015, s. 185-199
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Journal article (peer-reviewed)abstract
- A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graph wavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar grey matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity.
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| 2. |
- Behjat, Hamid
(author)
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Domain-Informed Signal Processing with Application to Analysis of Human Brain Functional MRI Data
- 2018
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Doctoral thesis (other academic/artistic)abstract
- Standard signal processing techniques are implicitly based on the assumption that the signal lies on a regular, homogeneous domain. In practice, however, many signals lie on an irregular or inhomogeneous domain. An application area where data are naturally defined on an irregular or inhomogeneous domain is human brain neuroimaging. The goal in neuroimaging is to map the structure and function of the brain using imaging techniques. In particular, functional magnetic resonance imaging (fMRI) is a technique that is conventionally used in non-invasive probing of human brain function. This doctoral dissertation deals with the development of signal processing schemes that adapt to the domain of the signal. It consists of four papers that in different ways deal with exploiting knowledge of the signal domain to enhance the processing of signals. In each paper, special focus is given to the analysis of brain fMRI data, either as the main theme (Paper I) or as proof of practical significance of the proposed schemes (Papers II, III and IV). Paper I presents a framework for enhanced fMRI activation mapping through exploiting filters that adapt to the brain anatomy. A novel procedure for constructing brain graphs, with subgraphs that separately encode the topology of the cerebral and cerebellar gray matter, is presented. Graph wavelets tailored to the convoluted boundaries of brain gray matter are designed and exploited to implement an anatomically-informed spatial transformation on fMRI data. Compared to conventional brain activation mapping schemes, the proposed approach shows superior type-I error control. Results on real data suggest a higher detection sensitivity as well as capability to capture subtle, connected patterns of brain activity. Paper II presents a graph-based signal decomposition scheme that adapts to the domain of the data as well as to the spectral content of a given signal set. The construction starts from the design of a prototype Meyer-type system of kernels with uniform subbands. The adaptivity of the approach is introduced by exploiting the ensemble energy spectral density. Using the ensemble energy spectral density, the prototype design is warped such that the resulting subbands each capture an equal amount of energy for the given signal class. Results on fMRI data and Monte Carlo simulations illustrate the superiority of signal-adapted frames over frames blind to signal characteristics in representing data and in denoising. Paper III presents a generic interpolation scheme for reconstructing signal samples from an inhomogeneous domain. The interpolation adapts to the inhomogeneity of the domain. The adaptation is incorporated by introducing a domain-similarity metric that characterises the domain in the adjacency of each sample point. The interpolation is shown to satisfy the domain-informed consistency principle, a principle that we define as an extension of the classical consistency principle. As proof of concept, domain-informed linear interpolation is presented as an extension of standard linear interpolation. Results from applying the proposed approach on fMRI data demonstrated its potential to reveal subtle details. Paper IV extends the theory in Paper III to enable reconstruction of signals with varying degrees of spatial smoothness. In particular, conventional shift-invariant B-spline interpolation is extended to a shift-variant, domain-informed interpolation. This is done by constructing a domain-informed generating basis that satisfies stability properties. The benefit of domain-informed interpolation over standard B-spline interpolation is demonstrated through Monte Carlo simulations across a range of B-spline orders. The practical significance of domain-informed spline interpolation is demonstrated on fMRI data. The results show the benefit of incorporating domain knowledge so that an interpolant consistent to the anatomy of the brain can be recovered by the proposed interpolation.
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| 3. |
- Behjat, Hamid, et al.
(author)
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Domain-Informed Spline Interpolation
- 2019
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In: IEEE Transactions on Signal Processing. - 1053-587X. ; 67:15, s. 3909-3921
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Journal article (peer-reviewed)abstract
- Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain tissue. We propose an interpolation method that instead exploits prior information about domain inhomogeneity, characterized by different, potentially overlapping, subdomains. As proof of concept, the focus is put on extending conventional shift-invariant B-spline interpolation. Given a known inhomogeneous domain, B-spline interpolation of a given order is extended to a domain-informed, shift-variant interpolation. This is done by constructing a domain-informed generating basis that satisfies stability properties. We illustrate example constructions of domain-informed generating basis and show their property in increasing the coherence between the generating basis and the given inhomogeneous domain. By advantageously exploiting domain knowledge, we demonstrate the benefit of domain-informed interpolation over standard B-spline interpolation through Monte Carlo simulations across a range of B-spline orders. We also demonstrate the feasibility of domain-informed interpolation in a neuroimaging application where the domain information is available by a complementary image contrast. The results show the benefit of incorporating domain knowledge so that an interpolant consistent to the anatomy of the brain is obtained.
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| 4. |
- Behjat, Hamid, et al.
(author)
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Signal-Adapted Tight Frames on Graphs
- 2016
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In: IEEE Transactions on Signal Processing. - 1053-587X. ; 64:22, s. 6017-6029
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Journal article (peer-reviewed)abstract
- The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different graph signal sets and are compared with non-signal-adapted frames. Vertex localization of a set of resulting atoms is studied. The frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising. The results illustrate the superiority of the designed signal-adapted frames, over frames blind to signal characteristics, in representing data and in denoising.
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| 5. |
- Behjat, Hamid, et al.
(author)
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Spectral design of signal-adapted tight frames on graphs
- 2019
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In: Signals and Communication Technology. - Cham : Springer International Publishing. - 1860-4862 .- 1860-4870. - 9783030035747 - 9783030035730 ; , s. 177-206
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Book chapter (peer-reviewed)abstract
- Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that we determine either directly using the graph Fourier transform or indirectly through approximation using a decomposition scheme. The approximation scheme has the benefit that (i) it does not require diagonalization of the Laplacian matrix, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is defined. The prototype design is then warped using the signal set’s ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations.
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| 6. |
- Behjat, Hamid
(author)
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Toolbox for enhanced fMRI activation mapping using anatomically adapted graph wavelets
- 2016
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Conference paper (peer-reviewed)abstract
- In fMRI studies with evoked activity, brain activity is detected by voxel-wise GLM tting, followed by statistical hypothesis testing. Statistical parametric mapping (SPM), one of the most popular classical methods, relies upon Gaussian smoothing to deal with the multiple-comparison correction. As an alternative, we have recently introduced a graph-based framework for fMRI brain activation mapping (Behjat, et al., 2015). The graph is designed such that it encodes the topological structure of the gray matter (GM). The approach exploits the spectral graph wavelet transform for the purpose of defining an advanced multi-scale spatial transformation for fMRI data. The use of spatial wavelet transforms has the benefit of providing a compact representation of activation patterns. The framework extends wavelet-based SPM (WSPM), which is a framework that combines wavelet processing of non-smoothed data with voxel-wise statistical testing while guaranteeing strong FP control. Here, we present an implementation of the proposed framework as a user-friendly, SPM-compatible toolbox that deals with multi-subject studies.
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| 7. |
- Maghsadhagh, Sevil, et al.
(author)
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Graph Spectral Characterization of Brain Cortical Morphology
- 2019
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In: 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). - 9781538613115 - 9781538613122
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Conference paper (peer-reviewed)abstract
- The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral metrics derived from these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the metrics are studied in the context of hemispheric asymmetry as well as gender dependent discrimination of cortical morphology.
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| 8. |
- Tarun, Anjali, et al.
(author)
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Graph spectral analysis of voxel-wise brain graphs from diffusion-weighted mri
- 2019
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In: 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019). - : IEEE. - 9781538636411 ; , s. 159-163
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Conference paper (peer-reviewed)abstract
- Non-invasive characterization of brain structure has been made possible by the introduction of magnetic resonance imaging (MRI). Graph modeling of structural connectivity has been useful, but is often limited to defining nodes as regions from a brain atlas. Here, we propose two methods for encoding structural connectivity in a huge brain graph at the voxel-level resolution (i.e., 850'000 voxels) based on diffusion tensor imaging (DTI) and the orientation density functions (ODF), respectively. The eigendecomposition of the brain graph's Laplacian operator is then showing highly-resolved eigenmodes that reflect distributed structural features which are in good correspondence with major white matter tracks. To investigate the intrinsic dimensionality of eigenspace across subjects, we used a Procrustes validation that characterizes inter-subject variability. We found that the ODF approach using 3-neighborhood captures the most in-formation from the diffusion-weighted MRI. The proposed methods open a wide range of possibilities for new research avenues, especially in the field of graph signal processing applied to functional brain imaging.
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