Evaluation of the Performance of Post-acquisition
Evaluation of the Performance of Post-acquisition Resolution Enhancement Methods for Magnetic Resonance Images Faezeh
1,2 Fallah ,
Denis Di
1 Franco ,
Fabian
3 Bamberg ,
Bin
1 Yang
1Institute of Signal Processing and System Theory, University of Stuttgart, Germany. 2Section on Experimental Radiology, University of Tubingen, Germany. 3Department of Diagnostic and Interventional Radiology, University of Tubingen, Germany. ¨ ¨
1. Introduction and Purpose MRI compromises between the acquirable spatial resolution, signal-to-noise-ratio (SNR), and scan time. High spatial resolution is required by most tissue segmentation and clustering purposes. This motivated development of post-acquisition super-resolution (SR) techniques that estimate an image of higher spatial resolution from multiple sub-voxel-shifted low-resolution images. Methods are proposed for SR estimation and acquisition of those low-resolution images were done by sub-pixel shifts of field-of-view or the excitation slice [1–5]. Besides reduction of scan time and motion artifacts, SR estimated images demonstrated higher SNRs than the directly acquired high-resolution images [6, 7]. In this work, we aimed to quantitatively evaluate the widely used SR techniques to demonstrate their best achievable performance. These quantitative evaluations were performed based on image fidelity metrics and independent of the strategy employed for acquisition of sub-voxel-shifted low-resolution images. To identify the optimum estimation technique and parameters, the estimation (optimization) method and the number of utilized low-resolution images and estimation iterations were varied.
2. Materials and Methods MR images were acquired from calf, breast, and trunk of 62 healthy volunteers using a 2D T1-weighted fast-spin-echo sequence and a 3D two-point Dixon VIBE sequence with different spatial resolutions and orientations. Those reference images were down-sampled, translated, and rotated to generate sub-voxel-shifted low-resolution images. Then high-resolution images were estimated from those low-resolution images and were compared with the reference images using some image fidelity metrics. The estimations were done by three most commonly used SR techniques. These techniques were based on an iterative back-projection (IBP) [1], a gradient descent optimization of the IBP (GDIBP) [2], and a least-square total variation minimization of the deterministic (L1 norm) regularized (L1-TVMDR) estimation of the high-resolution images [3].
Figure 2: Plots of the fidelity metrics for three SR algorithms calculated over MR images of 62 volunteers with regard to the number of low-resolution images.
Figure 3: Plots of the fidelity metrics for three SR algorithms calculated over MR images of 62 volunteers with regard to the number of estimation iterations.
Figure 1: The overall process of SR estimation techniques. The relationship between the lexicographically ordered sub-voxel-shifted lowresolution images Yk and the estimated high-resolution image X is given by [1–5]: Yk = Dk × Hk × Fk × X + Vk,
(1)
k = 1, ..., N,
where Dk is the down-sampling operator; Hk is the blurring operator; Fk is the geometric motion operator; and Vk is the additive white Gaussian noise.
Figure 4: Qualitative and quantitative performance of L1-TVMDR for different enhancement factors, 64 low-resolution images, and 50 estimation iterations.
3. Results
4. Conclusion
The considered SR techniques were quantitatively evaluated using fidelity metrics of mean structural similarity index (MSSIM) [8], mean squared errors (MSE) and SNR gain, comparing the estimated and the reference images. The structural similarity index (SSIM) is defined in terms of local means (µx, µy ), standard deviations (σx, σy ), and cross-covariance (σxy ) of reference and estimated images as: SSIM (x, y) =
(2µxµy + C1) · (2σxy + C2) (µ2x + µ2y + C1) · (σx2 + σy2 + C2)
.
In this work, three widely used SR algorithms were evaluated qualitatively and quantitatively independent of enhancement dimension, MR imaging protocol and contrast. Thus, the obtained results are of potential utility for selecting appropriate SR algorithm and estimation parameters which enhance spatial resolution of MR images a posterior, without adding artefactual effects.
(2)
Figure 2 and 3 show quantitative evaluations with regard to the number of utilized low-resolution images and the number of estimation iterations. As revealed, L1-TVMDR is the best performing algorithm. Also, minimum 64 low-resolution images and minimum 50 iterations led to its best performance. Figure 4 shows the qualitative and quantitative performance of L1-TVMDR algorithm for different enhancement factors while other parameters are kept optimum.
References: [1] Irani et al., ICPR 1990;2:115-120. Process. 2004;13:1327-1344. 2009;52:43-63.
[2] Zomet et al., CVPR 2001;1:645-650.
[3] Farsiu et al., IEEE Trans Image
[4] Fiat et al., 1997, U.S. Patent 6,294,914.
[5] Greenspan et al., Comput J.
[6] Plenge et al., SPIE Medical Imaging. 2012;8314.
2012;16:1465-1476.
[8] Wang et al., IEEE Trans. Image Process. 2004;13:600-612.
Contact information: [email protected] Presentation number: 183
ESMRMB 2016, Sept. 29 – Oct. 1, Vienna, Austria
[7] Scherrer et al., Med Image Anal.
1,2 Fallah ,
Denis Di
1 Franco ,
Fabian
3 Bamberg ,
Bin
1 Yang
1Institute of Signal Processing and System Theory, University of Stuttgart, Germany. 2Section on Experimental Radiology, University of Tubingen, Germany. 3Department of Diagnostic and Interventional Radiology, University of Tubingen, Germany. ¨ ¨
1. Introduction and Purpose MRI compromises between the acquirable spatial resolution, signal-to-noise-ratio (SNR), and scan time. High spatial resolution is required by most tissue segmentation and clustering purposes. This motivated development of post-acquisition super-resolution (SR) techniques that estimate an image of higher spatial resolution from multiple sub-voxel-shifted low-resolution images. Methods are proposed for SR estimation and acquisition of those low-resolution images were done by sub-pixel shifts of field-of-view or the excitation slice [1–5]. Besides reduction of scan time and motion artifacts, SR estimated images demonstrated higher SNRs than the directly acquired high-resolution images [6, 7]. In this work, we aimed to quantitatively evaluate the widely used SR techniques to demonstrate their best achievable performance. These quantitative evaluations were performed based on image fidelity metrics and independent of the strategy employed for acquisition of sub-voxel-shifted low-resolution images. To identify the optimum estimation technique and parameters, the estimation (optimization) method and the number of utilized low-resolution images and estimation iterations were varied.
2. Materials and Methods MR images were acquired from calf, breast, and trunk of 62 healthy volunteers using a 2D T1-weighted fast-spin-echo sequence and a 3D two-point Dixon VIBE sequence with different spatial resolutions and orientations. Those reference images were down-sampled, translated, and rotated to generate sub-voxel-shifted low-resolution images. Then high-resolution images were estimated from those low-resolution images and were compared with the reference images using some image fidelity metrics. The estimations were done by three most commonly used SR techniques. These techniques were based on an iterative back-projection (IBP) [1], a gradient descent optimization of the IBP (GDIBP) [2], and a least-square total variation minimization of the deterministic (L1 norm) regularized (L1-TVMDR) estimation of the high-resolution images [3].
Figure 2: Plots of the fidelity metrics for three SR algorithms calculated over MR images of 62 volunteers with regard to the number of low-resolution images.
Figure 3: Plots of the fidelity metrics for three SR algorithms calculated over MR images of 62 volunteers with regard to the number of estimation iterations.
Figure 1: The overall process of SR estimation techniques. The relationship between the lexicographically ordered sub-voxel-shifted lowresolution images Yk and the estimated high-resolution image X is given by [1–5]: Yk = Dk × Hk × Fk × X + Vk,
(1)
k = 1, ..., N,
where Dk is the down-sampling operator; Hk is the blurring operator; Fk is the geometric motion operator; and Vk is the additive white Gaussian noise.
Figure 4: Qualitative and quantitative performance of L1-TVMDR for different enhancement factors, 64 low-resolution images, and 50 estimation iterations.
3. Results
4. Conclusion
The considered SR techniques were quantitatively evaluated using fidelity metrics of mean structural similarity index (MSSIM) [8], mean squared errors (MSE) and SNR gain, comparing the estimated and the reference images. The structural similarity index (SSIM) is defined in terms of local means (µx, µy ), standard deviations (σx, σy ), and cross-covariance (σxy ) of reference and estimated images as: SSIM (x, y) =
(2µxµy + C1) · (2σxy + C2) (µ2x + µ2y + C1) · (σx2 + σy2 + C2)
.
In this work, three widely used SR algorithms were evaluated qualitatively and quantitatively independent of enhancement dimension, MR imaging protocol and contrast. Thus, the obtained results are of potential utility for selecting appropriate SR algorithm and estimation parameters which enhance spatial resolution of MR images a posterior, without adding artefactual effects.
(2)
Figure 2 and 3 show quantitative evaluations with regard to the number of utilized low-resolution images and the number of estimation iterations. As revealed, L1-TVMDR is the best performing algorithm. Also, minimum 64 low-resolution images and minimum 50 iterations led to its best performance. Figure 4 shows the qualitative and quantitative performance of L1-TVMDR algorithm for different enhancement factors while other parameters are kept optimum.
References: [1] Irani et al., ICPR 1990;2:115-120. Process. 2004;13:1327-1344. 2009;52:43-63.
[2] Zomet et al., CVPR 2001;1:645-650.
[3] Farsiu et al., IEEE Trans Image
[4] Fiat et al., 1997, U.S. Patent 6,294,914.
[5] Greenspan et al., Comput J.
[6] Plenge et al., SPIE Medical Imaging. 2012;8314.
2012;16:1465-1476.
[8] Wang et al., IEEE Trans. Image Process. 2004;13:600-612.
Contact information: [email protected] Presentation number: 183
ESMRMB 2016, Sept. 29 – Oct. 1, Vienna, Austria
[7] Scherrer et al., Med Image Anal.
