Dynamic MRI has been recognized as a promising method for visualizing articulatory motion of speech in scientific research and clinical applications¹. However, characterization of the gestural and acoustical properties of the vocal tract remains challenging because it requires: 1) reconstructing high-quality spatiotemporal images by incorporating strong prior knowledge; and 2) quantitatively interpreting the reconstructed images that contain great motion variability. This work presents a novel method that meets both requirements simultaneously by integrating a spatiotemporal atlas² into a Partial Separability³ (PS) model-based imaging framework. Through an atlas-driven group-sparsity constraint, this method achieves high-quality articulatory dynamics at an imaging speed of 102 frames per second (fps) and a spatial resolution of 2.2x2.2 mm². Moreover, this method enables quantitative characterization of motion variability, compared to the general motion pattern from all subjects, through the spatial residual components.

A key feature of the proposed method lies in the use of a spatiotemporal atlas, $$$I_a(\mathbf{r}, t)$$$, to capture the general pattern of articulatory motion across "all" subjects. As illustrated in Figure 1, a generic atlas has been created for statistical modeling of the vocal tract² and was utilized for dynamic speech imaging. Specifically, this atlas was constructed in a common space by spatially transforming the initial reconstructions from multiple subjects using group-wise diffeomorphic registrations⁴. In our application, this generic atlas was further converted into subject-specific atlas through Lipchitz-norm-based temporal warping² and diffeomorphic-mapping-based spatial warping⁵ procedures. The resulting atlas not only carries an objective description of the "expected" motion pattern for a specific subject, but also remains spatiotemporally in register with the target subject's articulatory motion.

The desired spatiotemporal image $$$I(\mathbf{r}, t)$$$ can be expressed in terms of $$$L^{th}$$$-order partially-separable functions³: $$I(\mathbf{r},t)=\sum_{l_{1}=1}^{L_{1}}\psi_{l_{1}}(\mathbf{r_{\mathrm{1}}})\phi_{l_{1}}(t)+\sum_{l_{2}=1}^{L_{2}}\psi_{l_{2}}(\mathbf{r_{\mathrm{2}}}) \phi_{l_{2}}(t),$$where $$$r_{\mathrm{1}}$$$ and $$$r_{\mathrm{2}}$$$ represent the spatial locations within and outside the articulatory movement region (determined from the atlas), $$$L_{1}$$$ and $$$L_{2}$$$ the model orders associated with $$$r_{\mathrm{1}}$$$ and $$$r_{\mathrm{2}}$$$, $$$\{\psi_{l_{1}}(\mathbf{r_{\mathrm{1}}})\}_{l_{1}=1}^{L_{1}}$$$ and $$$\{\psi_{l_{2}}(\mathbf{r_{\mathrm{2}}})\}_{l_{2}=1}^{L_{2}}$$$ the corresponding spatial coefficients, $$$\{\phi_{l_{1}}(t) \}_{l_{1}=1}^{L_{1}}$$$ and $$$\{\phi_{l_{2}}(t)\}_{l_{2}=1}^{L_{2}}$$$ the associated temporal basis functions. $$$I(\mathbf{r}, t)$$$ can be reconstructed from highly-undersampled data $$$d(\mathbf{r},t)$$$ by jointly enforcing the regional low-rank constraint with a group-sparsity constraint driven by the spatiotemporal atlas $$$I_a(\mathbf{r},t)$$$⁴. The reconstruction problem is formulated as:$$\hat{\mathbf{\mathrm{I}}}=\mathrm{argmin}||\mathbf{\mathrm{d}}-\mathbf{\mathrm{E}}(\mathbf{\mathrm{I}})||_{2}^{2}+\mathrm{\lambda}||\mathbf{\mathrm{I}}-\mathbf{\mathrm{I}}_a||_{1,2},$$where $$$\mathbf{\mathrm{E}}(\mathbf{\cdot})$$$ represents an encoding operator encompassing sparse sampling, regional low-rank modeling and parallel imaging, $$$\mathrm{\lambda}$$$ represents a regularization parameter. An algorithm based on half-quadratic regularization has been applied to solve this optimization problem.¹

To demonstrate the effectiveness of the proposed method, experiments were performed following a PS model-based acquisition strategy¹ to sparsely sample the $$$(\mathbf{k},t)$$$-space. A FLASH sequence (TR = 9.78ms) integrating a cone-trajectory navigator acquisition (TE = 0.85ms) and Cartesian imaging acquisition (TE = 2.30ms) was implemented on a Siemens Trio 3T scanner to acquire data over a 260x260 mm² FOV with a 12-channel head receiver coil. During data acquisition, three volunteer subjects were requested to produce repetitive /loo/-/lee/-/la/-/za/-/na/-/za/ sounds at their natural speaking rates in accordance with the local IRB. Initial reconstructions from all subjects were input into the atlas formation procedure to enable spatiotemporal alignment of articulatory motion. The final reconstructions had a matrix size of 128x128, a spatial resolution of 2.2x2.2 mm² and a nominal frame rate of 102 fps covering the upper vocal tract.

Figure 2a compares the reconstruction, the subject-specific atlas and the associated residual component. As is seen, the atlas captures the general articulatory motion, while the detailed structural differences at the tongue tip and velum (indicated with arrows) are picked up as residual components by the proposed sparsity constraint. Figure 2b and 2c compares the associated temporal profiles - the reconstruction captures richer spatiotemporal dynamics and sharper temporal transition as compared to the atlas. Figure 3 shows the envelopes of tongue contours for the reconstruction and the atlas from all /a/ sounds in $$$\mathbf{r_{\mathrm{1}}}$$$ (indicated with green color) in the production of /loo/-/lee/-/la/-/za/-/na/-/za/ phrases. The atlas tongue envelopes (pink) are approximately spatiotemporally aligned with the reconstruction envelopes (aqua), but demonstrates reduced motion variance due to the "averaging" effect from atlas creation².

This work presents a novel dynamic speech MRI method to capture articulatory movements with improved spatiotemporal dynamics and enhanced interpretability of motion. This is achieved by utilizing a spatiotemporal atlas to simultaneously provide strong prior information and promote spatiotemporal sparsity in regional low-rank model-based reconstructions. The proposed method not only allows high-quality reconstruction of articulator motion at a temporal frame rate of 102 fps and a spatial resolution of 2.2 x 2.2 mm², but also provides a platform to quantitatively characterize the target subject's articulatory motion with respect to the general motion pattern from all subjects.