Real‐time dynamic <scp>MR</scp> image reconstruction using compressed sensing and principal component analysis (<scp>CS</scp>‐<scp>PCA</scp>): Demonstration in lung tumor tracking

PURPOSE: This work presents a real-time dynamic image reconstruction technique, which combines compressed sensing and principal component analysis (CS-PCA), to achieve real-time adaptive radiotherapy with the use of a linac-magnetic resonance imaging system. METHODS: Six retrospective fully sampled dynamic data sets of patients diagnosed with non-small-cell lung cancer were used to investigate the CS-PCA algorithm. Using a database of fully sampled k-space, principal components (PC's) were calculated to aid in the reconstruction of undersampled images. Missing k-space data were calculated by projecting the current undersampled k-space data onto the PC's to generate the corresponding PC weights. The weighted PC's were summed together, and the missing k-space was iteratively updated. To gain insight into how the reconstruction might proceed at lower fields, 6× noise was added to the 3T data to investigate how the algorithm handles noisy data. Acceleration factors ranging from 2 to 10× were investigated using CS-PCA and Split Bregman CS for comparison. Metrics to determine the reconstruction quality included the normalized mean square error (NMSE), as well as the dice coefficients (DC) and centroid displacement of the tumor segmentations. RESULTS: Our results demonstrate that CS-PCA performed superior than CS alone. The CS-PCA patient averaged DC for 3T and 6× noise added data remained above 0.9 for acceleration factors up to 10×. The patient averaged NMSE gradually increased with increasing acceleration; however, it remained below 0.06 up to an acceleration factor of 10× for both 3T and 6× noise added data. The CS-PCA reconstruction speed ranged from 5 to 20 ms (Intel i7-4710HQ CPU @ 2.5 GHz), depending on the chosen parameters. CONCLUSIONS: A real-time reconstruction technique was developed for adaptive radiotherapy using a Linac-MRI system. Our CS-PCA algorithm can achieve tumor contours with DC greater than 0.9 and NMSE less than 0.06 at acceleration factors of up to, and including, 10×. The reconstruction speed for the Split Bregman CS ranged from 200 to 260 ms, whereas the CS-PCA reconstruction speed ranged from 5 to 20 ms implemented using nonoptimized MATLAB code.

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