Real-Time Optimized Reconstruction Algorithm
for Adaptive Imaging
J. M. SANTOS, G. A. WRIGHT AND J. M. PAULY
Department of Electrical Engineering, Stanford University, Stanford, CA, U S A
ASL-West, GE Medical Systems, Menlo Park, CA, U S A
A reconstruction algorithm for a real-time system requires
minimum latency and high speed to avoid introducing lag
and to be able to reconstruct images at the incoming data rate.
We propose an algorithm that takes advantage of some redundancies present on a continuous acquisition system and
does not require 2 x oversampling or 2N grid sizes. A look
up table method, partial reconstruction for view sharing and
parameter-optimizations based on a performance vs. quality
requirement provide a significant increase in performance as
well as flexibility for adaptive imaging, scalability for multi
coil acquisitions and minimum hardware requirements.
Introduction: Image reconstruction in a real-time system normally involves re-gridding from non Cartesian samples [1,2] and
obtaining the Fourier transformed data. These two well-known
algorithms are computationallyintensive and create a speed limitation that has been overcomeby special hardware or distributed
computer systems [3]. An important requirement for this reconstruction process is that it has to be done fast enough in order to
maintain the rate at which the data are acquired. Another requirement is to have minimum latency for responsiveness.
We have developed an algorithm that achieves both requirements, providing flexibility for adaptive imaging, scalability for
parallel acquisitions and minimum hardware requirements.
Methods: In a real-time system, where images are acquired continuously, some redundancies can be exploited to increase performance:
Repeated k-space trajectory. The gridding algorithm involves
computing a convolution sum between the sampled data and a
filtering kernel function. Dale et al. [4] proposed to use a lookup
table to precompute the filtering function so the gridding operation is reduced to a weighted sum of the sampled values at the
grid locations. This allows us to implement computationally intensive filters like Kaiser-Bessel without affecting the gridding
performance while adding only a small latency.
Viewsharing. To improve the perceived quality of the real-time
system, images are usually reconstructed using a sliding window
algorithm 151. Images are generated by sharing acquisitions between consecutive full frame acquisitions. As only a fraction of
the data are needed for each new image, we propose a method
that reconstructs the image without regridding a full data set.
The proposed method saves all the data from the previously
reconstructed image. To reconstruct the next frame we just regrid the differencebetween the new data and the corresponding
acquisitions from the previous image. Since the gridding convolution is a linear operation, adding this gridded data to the previous frame results in a new set that will correspond to the desired
sliding window data (Fig. 1). This method reduces the gridding
time by a proportion of the number of shared acquisitions and the
complete data set.
Corresponding
Previons
gridded data
New gridded data
Figure 1: Sliding window partial reconstruction algorithm
Another opportunity for speedup is greater flexibility in parameter optimization. One of the main considerations when designing a reconstruction algorithm has been to use a zN grid
sue so the FFT algorithm can be efficiently used. A tradeoff between speed and quality determines then the appropriate window width to use.
© Proc. Intl. Soc. Mag. Reson. Med. 10 (2002)
Highly optimized algorithms like FFTW 161, provide a wider
range of matrix sizes for which the computation speed can be
compared to power of two matrices. This situation provides an
extra degree of freedom in the parameter design. When using
a Kaiser-Bessel kernel, traditional parameters (2 x oversampling,
width 3) gives aliasing error levels below 10-l'. It is then possible
to reduce the oversampling ratio and the window width to find a
combinationthat maximizesperformance providing a reasonable
level of aliasing energy [7]
The reconstruction algorithm was implemented on a 1.2 GHz
AMD Athlon processor for a spiral localizer sequence of 6 interleaves, 1536 samples, 20 cm FOV, 1.9 mm resolution and 30 ms
TR.
Results and Discussion:Figure2 shows one frame from the localizer sequence reconstructed at maximum speed. The implementation was able to obtain speeds of 50 fps doing full reconstruction
at 256 x 256, oversampling 2 . 4 ~and kernel width of 3 samples.
220 f p s for sliding window optimized at 160 x 160, oversampling
1.5 x and width 3. This performance allows process multi-coil acquisitions without the need for extra computing power.
Figure 2: Localizer image reconstructed at 50 f p s and at 220 f p s
sliding window optimized.
The sliding window partial reconstruction is mathematically
equivalent to full reconstruction. Accumulation of numerical error can be a problem. However after reconstruction of 400 frames,
we observe a negligible relative mean square error of
As computer complexity increases, the number of operations
is not the best measure of an algorithmperformance. We observed
that for a 256 x 256 matrix, the FFT time was 7.57 ms, but for
252 x 252 it was 4.68 ms which represents a 38% increase in performance for a 3% decrease in the number of points. Even for
bigger matrices performance can be better, 260 x 260 at 5.14 ms.
Conclusion: The algorithm provides adequate performance for
real-time imaging using standard hardware. Scalability is
achieved with parallel reconstruction processes for multi coil acquisitions. The algorithm allows for adaptive imaging as fundamental changes in the acquisition, like changing the k-space trajectory, can be handled by simply recomputing the lookup table.
The combination of using look-up-table, partial sliding window reconstruction, proper choice of grid size and Kaiser-Bessel
width leads to high speed reconstructionwithout affecting image
quality.
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