DOI QR코드

DOI QR Code

Image Denoising for Metal MRI Exploiting Sparsity and Low Rank Priors

  • Choi, Sangcheon (Department of Computational Science and Engineering, Yonsei University) ;
  • Park, Jun-Sik (Department of Biomedical Engineering, Sungkyunkwan University) ;
  • Kim, Hahnsung (Department of Biomedical Engineering, Sungkyunkwan University) ;
  • Park, Jaeseok (Department of Biomedical Engineering, Sungkyunkwan University)
  • Received : 2016.10.10
  • Accepted : 2016.12.05
  • Published : 2016.12.31

Abstract

Purpose: The management of metal-induced field inhomogeneities is one of the major concerns of distortion-free magnetic resonance images near metallic implants. The recently proposed method called "Slice Encoding for Metal Artifact Correction (SEMAC)" is an effective spin echo pulse sequence of magnetic resonance imaging (MRI) near metallic implants. However, as SEMAC uses the noisy resolved data elements, SEMAC images can have a major problem for improving the signal-to-noise ratio (SNR) without compromising the correction of metal artifacts. To address that issue, this paper presents a novel reconstruction technique for providing an improvement of the SNR in SEMAC images without sacrificing the correction of metal artifacts. Materials and Methods: Low-rank approximation in each coil image is first performed to suppress the noise in the slice direction, because the signal is highly correlated between SEMAC-encoded slices. Secondly, SEMAC images are reconstructed by the best linear unbiased estimator (BLUE), also known as Gauss-Markov or weighted least squares. Noise levels and correlation in the receiver channels are considered for the sake of SNR optimization. To this end, since distorted excitation profiles are sparse, $l_1$ minimization performs well in recovering the sparse distorted excitation profiles and the sparse modeling of our approach offers excellent correction of metal-induced distortions. Results: Three images reconstructed using SEMAC, SEMAC with the conventional two-step noise reduction, and the proposed image denoising for metal MRI exploiting sparsity and low rank approximation algorithm were compared. The proposed algorithm outperformed two methods and produced 119% SNR better than SEMAC and 89% SNR better than SEMAC with the conventional two-step noise reduction. Conclusion: We successfully demonstrated that the proposed, novel algorithm for SEMAC, if compared with conventional de-noising methods, substantially improves SNR and reduces artifacts.

Keywords

References

  1. Cho ZH, Kim DJ, Kim YK. Total inhomogeneity correction including chemical shifts and susceptibility by view angle tilting. Med Phys 1988;15:7-11 https://doi.org/10.1118/1.596162
  2. Koch KM, Lorbiecki JE, Hinks RS, King KF. A multispectral three-dimensional acquisition technique for imaging near metal implants. Magn Reson Med 2009;61:381-390 https://doi.org/10.1002/mrm.21856
  3. Lu W, Pauly KB, Gold GE, Pauly JM, Hargreaves BA. SEMAC: Slice Encoding for Metal Artifact Correction in MRI. Magn Reson Med 2009;62:66-76 https://doi.org/10.1002/mrm.21967
  4. Lu W, Pauly KB, Gold GE, Pauly JM, Hargreaves BA. Slice encoding for metal artifact correction with noise reduction. Magn Reson Med 2011;65:1352-1357 https://doi.org/10.1002/mrm.22796
  5. Candes EJ, Recht B. Exact matrix completion via convex optimization. Found Comput Math 2009;9:717-772 https://doi.org/10.1007/s10208-009-9045-5
  6. Cai JF, Candes EJ, Shen Z. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization 2010;20:1956-1982 https://doi.org/10.1137/080738970
  7. Lee K, Bresler Y. ADMiRA: atomic decomposition for minimum rank approximation. IEEE Trans Inf Theory 2010;56:4402-4416 https://doi.org/10.1109/TIT.2010.2054251
  8. Lee K, Bresler Y. Guaranteed minimum rank approximation from linear observations by nuclear norm minimization with ellipsoidal constraint. arXiv preprint arXiv:0903.4742, 2009
  9. Erez Y, Schechner YY, Adam D. Space variant ultrasound frequency compounding based on noise characteristics. Ultrasound Med Biol 2008;34:981-1000 https://doi.org/10.1016/j.ultrasmedbio.2007.11.012
  10. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn Reson Med 1999;42:952-962 https://doi.org/10.1002/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S
  11. Blaimer M, Breuer F, Mueller M, Heidemann RM, Griswold MA, Jakob PM. SMASH, SENSE, PILS, GRAPPA: how to choose the optimal method. Top Magn Reson Imaging 2004;15:223-236 https://doi.org/10.1097/01.rmr.0000136558.09801.dd
  12. Donoho DL. Compressed sensing. IEEE Trans Inf Theory 2006;52:1289-1306 https://doi.org/10.1109/TIT.2006.871582
  13. Daubechies I, Defrise M, De Mol D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl 2004;57:1413-1457 https://doi.org/10.1002/cpa.20042
  14. Lustig M, Donoho D, Pauly JM. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 2007;58:1182-1195 https://doi.org/10.1002/mrm.21391
  15. Davis G, Mallat S, Avellaneda M. Adaptive greedy approximation. Constr Approx 1997;13:57-98 https://doi.org/10.1007/BF02678430
  16. Tropp JA. Greed is good: algorithmic results for sparse approximation. IEEE Trans Inform Theory 2004;50:2231-2242 https://doi.org/10.1109/TIT.2004.834793
  17. Figueiredo MAT, Nowak RD, Wright SJ. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Sel Top Signal Process 2007;1:586-597 https://doi.org/10.1109/JSTSP.2007.910281
  18. Tropp JA, Gilbert AC. Signal revocery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 2007;53:4655-4666 https://doi.org/10.1109/TIT.2007.909108
  19. Gamper U, Boesiger P, Kozerke S. Compressed sensing in dynamic MRI. Magn Reson Med 2008;59:365-373 https://doi.org/10.1002/mrm.21477
  20. Chen SS, Donoho DL, Saunders MA. Atomic decomposition by basis pursuit. SIAM Review 2001;43:129-159 https://doi.org/10.1137/S003614450037906X

Cited by

  1. Susceptibility Artifact를 감소시키는 SEMAC 사용 시 Turbo Factor 변화에 따른 영상의 유용성 평가 vol.13, pp.1, 2019, https://doi.org/10.7742/jksr.2019.13.1.31