Highly constrained backprojection for time-resolved MRI

Abstract

Recent work in k-t BLAST and undersampled projection angiography has emphasized the value of using training data sets obtained during the acquisition of a series of images. These techniques have used iterative algorithms guided by the training set information to reconstruct time frames sampled at well below the Nyquist limit. We present here a simple non-iterative unfiltered backprojection algorithm that incorporates the idea of a composite image consisting of portions or all of the acquired data to constrain the backprojection process. This significantly reduces streak artifacts and increases the overall SNR, permitting decreased numbers of projections to be used when acquiring each image in the image time series. For undersampled 2D projection imaging applications, such as cine phase contrast (PC) angiography, our results suggest that the angular undersampling factor, relative to Nyquist requirements, can be increased from the present factor of 4 to about 100 while increasing SNR per individual time frame. Results are presented for a contrast-enhanced PR HYPR TRICKS acquisition in a volunteer using an angular undersampling factor of 75 and a TRICKS temporal undersampling factor of 3 for an overall undersampling factor of 225.

FIG. 1

Schematic diagram of the HYPR reconstruction algorithm. For simplicity, the diagram shows a single projection for each time frame. A 1D Fourier Transform converts the radial k-space lines to projections in image space. A composite image is reconstructed from the projections in all time frames. For each individual HYPR time frame, the composite image is multiplied by the unfiltered backprojected profile P specific to the time frame normalized by the corresponding unfiltered backprojected profile P_c calculated from the composite image.

FIG. 2

Illustration of the HYPR algorithm for the case of 3D VIPR. Each projection profile value is distributed in the Radon plane perpendicular to the profile in proportion to the signal present in the composite image. Shown here is a Radon plane at radius r, polar angle θ, and azimuthal angle ϕ. P (r,θ,ϕ) is the projection value representing the sum of signals in the plane.

FIG. 3

Images from the modulated time series used for Simulation 1. The right side of the image is constant in time. The left side is sinusoidally modulated in time.

FIG. 4

Illustration of the formation of progressive composite images for use in contrast enhanced time-resolved angiography. The first composite is formed from 2 or more time frames. As additional time frames are acquired, their information is added to the composite image.

FIG. 5

Comparison of under-sampled standard filtered back-projection (FBP) and HYPR images formed from 4, 6, 8, and 10 projections. A time series containing 16 frames was used in this example.

FIG. 6

Comparison of 10-projection HYPR image (a) with an image formed as a product of a 10-projection FBP multiplied by the composite image (b). The image in (b) retains the basic FBP intravascular streak artifacts.

FIG. 7

Comparison of programmed (Actual) waveform with those obtained from FBP and HYPR images with 4, 6, 8, and 10 projections for the modulated side of the image. The FBP waveforms are initially underestimated but are close to the HYPR waveforms for 10 projections and above.

FIG. 8

Comparison of programmed (Actual) waveform with those obtained from FBP and HYPR images with 4, 6, 8, and 10 projections for the unmodulated side of the image. Once again the FBP values underestimate the Actual constant waveform. The HYPR waveform shows some contamination from the left side in this example of spatial variation of the temporal waveform.

FIG. 9

Comparison of image quality of an undersampled FBP image obtained with 40 projections with that of HYPR images obtained with various numbers of projections (pr) and numbers of frames (fr) in the time series. For a 30-frame acquisition, the HYPR technique provides a factor of 100 undersampling factor. Image quality is better than the FBP technique, which provides a factor of 10 undersampling factor relative to a fully sampled (400 projection) image. For the same number of projections, the FBP and HYPR images require equal acquisition times. Total scan time is proportional to the product of the number of projections and number of frames. Undersampling factors are shown on the right.

FIG. 10

(a) Simulation 3. Top row: frames 2, 4, 6, and 8 from a clinical PR TRICKS examination that used 150 projections per time frame. Middle row: 30 projection FBP with undersampling factor of 13. Severe streaks are evident. Bottom row: 30 projection HYPR images. Image quality improves later in the exam because of increased projections in the composite image. (b) Signal curves for Simulation 3. FBP and HYPR signals are higher than Actual for the first 2 frames due to background signal. HYPR estimate improves as frames are added to the composite image.

FIG. 11

Every tenth frame of a PR TRICKS time series using 10 projections per 940ms time frame. The combined k-t undersampling factor = 225. Conventional PR TRICKS is shown in (a). HYPR PR TRICKS is shown in (b).

FIG. 12

Time frame acceleration factors for several acquisition techniques. The acceleration factors indicate the time savings for individual time frames relative to fully sampled radial acquisition. Scan time is the product of this time and the number of frames. HYPR acceleration factor estimates presume a time series of 10–30 time frames. Acceleration factors do not includethe potential benefits of combination with parallel imaging techniques. HYPR acquisition parameters have been chosen to maintain current image quality in spite of higher accelerations.