Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging

A predictive signal model for dynamic cardiac magnetic resonance imaging

Robust dynamic cardiac magnetic resonance imaging (MRI) has been a long-standing endeavor-as real-time imaging can provide information on the temporal signatures of disease we currently cannot assess-with the past decade seeing remarkable advances in acceleration using compressed sensing (CS) and artificial intelligence (AI). However, substantial limitations to real-time imaging remain and reconstruction quality is not always guaranteed. To improve reconstruction fidelity in dynamic cardiac MRI, we propose a novel predictive signal model that uses a priori statistics to adaptively predict temporal cardiac dynamics. By using a small training set obtained from the same patient, the new signal model can achieve robust dynamic cardiac MRI in the presence of irregular cardiac rhythm. Evaluation on simulated irregular cardiac dynamics and prospectively undersampled clinical cardiac MRI data demonstrate improved reconstruction quality for two reconstruction frameworks: Kalman filter and CS. The predictive model also works with different undersampling patterns (cartesian, radial, spiral) and can serve as a versatile foundation for robust dynamic cardiac MRI.

Comparison of nonlinear filtering techniques for photonic systems with blackbody radiation

This work explores a theoretical solution for noise reduction in photonic systems using blackbody radiators. Traditionally, signal noise can be reduced by increasing the integration time during signal acquisition. However, increasing the integration time during signal acquisition will reduce the acquisition speed of the signal. By developing and applying a filter using a model based on the theoretical equations for blackbody radiation, the noise of the signal can be reduced without increasing integration time. In this work, three filters, extended Kalman filter, unscented Kalman filter (UKF), and extended sliding innovation filter (ESIF), are compared for blackbody photonic systems. The filters are tested on a simulated signal from five scenarios, each simulating different experimental conditions. In particular, the nonlinear filters, UKF and ESIF, showed a significant reduction of noise from the simulated signal in each scenario. The results show great promise for photonic systems using blackbody radiators that require post-process for noise reduction.

Assessment of velopharyngeal function with dual-planar high-resolution real-time spiral dynamic MRI

PURPOSE

To develop a real-time dynamic MRI method for comprehensive evaluation of velum movement during speech.

METHODS

Dynamic MRI has been used to study velopharyngeal insufficiency (VPI) by imaging the movement of the velum during speech, because it can provide good anatomic details with no exposed radiation. To be able to comprehensively evaluate dynamic velum movement, a real-time spiral non-balanced SSFP sequence was developed with simultaneous dual-planar coverage and improved spatial and temporal resolution using a combination of parallel imaging and spatial and temporal compressed sensing to achieve 6 × acceleration. New off-resonance correction and post-processing methods were also developed to reduce blurring and slice crosstalk.

RESULTS

The method demonstrated good image quality for visualizing dynamic velum movement with reduced blurring and improved image homogeneity. Spatial resolution of 1.2*1.2 mm² with 150 mm FOV and temporal resolution of 20 frames-per-second with simultaneous dual-planar coverage was achieved.

CONCLUSIONS

This work describes a new technique for studying speech disorders using dual-planar accelerated spiral dynamic MRI.

Causal MRI reconstruction via Kalman prediction and compressed sensing correction

This technical note addresses the problem of causal online reconstruction of dynamic MRI, i.e. given the reconstructed frames till the previous time instant, we reconstruct the frame at the current instant. Our work follows a prediction-correction framework. Given the previous frames, the current frame is predicted based on a Kalman estimate. The difference between the estimate and the current frame is then corrected based on the k-space samples of the current frame; this reconstruction assumes that the difference is sparse. The method is compared against prior Kalman filtering based techniques and Compressed Sensing based techniques. Experimental results show that the proposed method is more accurate than these and considerably faster.

Direct and accelerated parameter mapping using the unscented Kalman filter

PURPOSE

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem.

METHODS

In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling.

RESULTS

Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies.

CONCLUSION

This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping.

Accelerated dynamic cardiac MRI exploiting sparse-Kalman-smoother self-calibration and reconstruction (k - t SPARKS)

Accelerated dynamic MRI, which exploits spatiotemporal redundancies in k  -  t space and coil dimension, has been widely used to reduce the number of signal encoding and thus increase imaging efficiency with minimal loss of image quality. Nonetheless, particularly in cardiac MRI it still suffers from artifacts and amplified noise in the presence of time-drifting coil sensitivity due to relative motion between coil and subject (e.g. free breathing). Furthermore, a substantial number of additional calibrating signals is to be acquired to warrant accurate calibration of coil sensitivity. In this work, we propose a novel, accelerated dynamic cardiac MRI with sparse-Kalman-smoother self-calibration and reconstruction (k  -  t SPARKS), which is robust to time-varying coil sensitivity even with a small number of calibrating signals. The proposed k  -  t SPARKS incorporates Kalman-smoother self-calibration in k  -  t space and sparse signal recovery in x  -   f space into a single optimization problem, leading to iterative, joint estimation of time-varying convolution kernels and missing signals in k  -  t space. In the Kalman-smoother calibration, motion-induced uncertainties over the entire time frames were included in modeling state transition while a coil-dependent noise statistic in describing measurement process. The sparse signal recovery iteratively alternates with the self-calibration to tackle the ill-conditioning problem potentially resulting from insufficient calibrating signals. Simulations and experiments were performed using both the proposed and conventional methods for comparison, revealing that the proposed k  -  t SPARKS yields higher signal-to-error ratio and superior temporal fidelity in both breath-hold and free-breathing cardiac applications over all reduction factors.

Motion-compensated compressed sensing for dynamic contrast-enhanced MRI using regional spatiotemporal sparsity and region tracking: block low-rank sparsity with motion-guidance (BLOSM)

PURPOSE

Dynamic contrast-enhanced MRI of the heart is well-suited for acceleration with compressed sensing (CS) due to its spatiotemporal sparsity; however, respiratory motion can degrade sparsity and lead to image artifacts. We sought to develop a motion-compensated CS method for this application.

METHODS

A new method, Block LOw-rank Sparsity with Motion-guidance (BLOSM), was developed to accelerate first-pass cardiac MRI, even in the presence of respiratory motion. This method divides the images into regions, tracks the regions through time, and applies matrix low-rank sparsity to the tracked regions. BLOSM was evaluated using computer simulations and first-pass cardiac datasets from human subjects. Using rate-4 undersampling, BLOSM was compared with other CS methods such as k-t SLR that uses matrix low-rank sparsity applied to the whole image dataset, with and without motion tracking, and to k-t FOCUSS with motion estimation and compensation that uses spatial and temporal-frequency sparsity.

RESULTS

BLOSM was qualitatively shown to reduce respiratory artifact compared with other methods. Quantitatively, using root mean squared error and the structural similarity index, BLOSM was superior to other methods.

CONCLUSION

BLOSM, which exploits regional low-rank structure and uses region tracking for motion compensation, provides improved image quality for CS-accelerated first-pass cardiac MRI.