Method for Reduction of Reconstruction Time for Compressed Sensing of Multi-Image Series
Andrew J Wheaton1, Samir D Sharma1, and Antonios Matakos1

1Canon Medical Research USA, Mayfield, OH, United States


This proof-of-concept study demonstrates a method to reduce CS reconstruction time for multi-image series (e.g. relaxometry mapping, multi-echo, or dynamic) by leveraging the similarity of data across the image series. The method consists of two components: a) re-using auto-calibrated coil sensitivity maps computed from data of the first image[0] and b) warm starting the iterative reconstruction of each image[i] using the final output from the reconstruction of the previous image[i-1] in the series. One insight is a ‘hybrid warm start’ created by combining the magnitude from the previous image[i-1] reconstruction and the phase of the back-projection of the current image[i].


The purpose of this proof-of-concept study is to demonstrate a method to reduce reconstruction time of compressed sensing (CS) [1] for multi-image series.


For multi-image series applications, including relaxometry mapping, multi-echo, or dynamic, the CS reconstruction problem becomes proportionally larger in time and/or memory. Using conventional approaches, each image in the series would be reconstructed separately. In practice, the finite amount of available memory prohibits parallelizing the reconstruction of multiple images simultaneously. Therefore, for example, a four-echo series would take 4X longer as compared to a single-echo acquisition. This proof-of-concept study proposes a method to reduce CS reconstruction time by leveraging the similarity of data across the image series.


The implementation of CS demonstrated in this study includes ESPIRiT coil sensitivity maps generated from a fully-sampled central region of k-space [2]. FISTA is used to solve the minimization problem [3].

The first speedup improvement is to re-use the ESPIRiT coil maps estimated from the first image of the series. Since ESPIRiT maps are eigenvalue-based, they are largely immune from variation in signal contrast and phase across the image series.

The second speedup improvement is to use the final image output from the previous echo as the starting point for the iterative process of the next echo. This re-use of image data to start the next series is an example of a ‘warm start’ – as opposed to a ‘cold start’ where the starting image is the zero-filled back projection of the undersampled k-space data. The warm start approach leverages the observation that image structure and contrast is largely similar between two adjacent images in a series. The warm start enables a faster convergence (fewer iterations) enabling further reduction of computation time.

In our study, a hybrid approach to a warm start proved most beneficial. In the ‘hybrid warm start,’ the magnitude from the previous image is combined with the phase of the back-projection of the current image. We observed that the phase data of two adjacent images in a multi-echo series can be quite different, largely due to background phase evolution between the two echoes. Relatedly, the phase information of the initial back-projection is close to the phase of the final iterative solution. This phenomenon is caused by two characteristics of a CS acquisition: a) low spatial frequency k-space is fully (or nearly fully) sampled and b) phase variation is largely low spatial frequency. In other words, there is little improvement needed in the phase data compared to the initial back-projection data. Figure 1 illustrates this observation.

To demonstrate this technical method, multi-echo field echo data of cervical spine of a healthy volunteer were acquired on a Canon Medical Titan 3T scanner using a 16 channel head-neck coil under IRB approval. The image data were 0.8x0.8x2.0mm3 with matrix size = 256x256x80 and 2x2 undersampling in phase x slice encode directions. Four echoes were acquired with flyback readout using echo spacing 4.6ms. CS reconstruction was performed on a machine running Ubuntu Linux 18.04 equipped with an 8-core Intel Xeon E5-2620 processor, 96 GB RAM and an NVIDIA P5000 GPU.


Figure 2 displays the comparison of image quality for hybrid warm start vs. cold start. It can be observed that cold start images are noticeably blurrier than hybrid warm start images in the early iterations. The visual observation is supported by RMSE and SSI metrics (Figure 3). In our example, the two approaches matched after approximately 20 iterations. The image output of all echoes for both approaches is displayed in Figure 4.

Using conventional reconstruction, the total time for the 4-echo series was 65 seconds. By reusing the ESPIRiT map, reconstruction time was reduced to 42 seconds. The potential for further time savings with reduction of iterations due to hybrid warm start is described in Discussion.


The reconstruction time improvement achievable with this method is dependent on the clinical application, acceleration factor, and desired image quality. In our example, warm start outperformed cold start until approximately 20 iterations. For other clinical applications or acceleration factors, the performance of warm start vs. cold start may vary. Depending on desired image quality, the number of iterations may be reduced when using the hybrid warm start approach.

The limitations of this proof-of-concept study are many. Most importantly, only one clinical application at a fixed acceleration factor was analyzed. The focus of this abstract is to propose a general strategy – the details of the implementation of this method and the potential reconstruction time savings are expected to vary per clinical application.


No acknowledgement found.


[1] Lustig M, Donoho D, Pauly JM. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med 2007; 58: 1182-1195.

[2] Uecker M, et al. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA. Magn Reson Med 2014; 71: 990-1001.

[3] Beck A, Teboulle M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans Image Process 2009; 18: 2419–2434.


Figure 1: Magnitude and phase images of cold start (back-projection of undersampled data from second echo), non-hybrid warm start (using the phase from the first echo), hybrid warm start (magnitude from warm start and phase from cold start), and final output of the conventional solution. The small variation in magnitude between non-hybrid warm start (same as hybrid warm start) and final output is observable. However, the phase of non-hybrid warm start and final output are different. In contrast, the phase image of the cold start (same as hybrid warm start) and final output are similar. This observation led to the ‘hybrid warm start’ approach.

Figure 2: Comparison of image output for hybrid warm start vs. cold start for the second echo in a cervical spine multi-echo image series. The reference image is the final output (after 100 iterations) with cold start.

Figure 3: Comparison of RMSE and SSIM for hybrid vs. cold start for the region of interest drawn on the spinal cord in Figure 2.

Figure 4: Comparison of image output of cold start vs. hybrid warm start for four-echo image series at iteration #20.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)