劉元元，楊育昕,2，朱慶永，崔卓須，程 靜，劉聰聰，梁 棟,，朱燕杰*

基于多弛豫信號補(bǔ)償?shù)目焖俅殴舱?散布成像

劉元元1，楊育昕1,2，朱慶永3，崔卓須3，程 靜1，劉聰聰1，梁 棟1,3，朱燕杰1*

1. 保羅C.勞特伯生物醫(yī)學(xué)成像研究中心，中國科學(xué)院深圳先進(jìn)技術(shù)研究院，廣東 深圳 518055；2. 藥學(xué)與生物工程學(xué)院，重慶理工大學(xué)，重慶 400054；3. 醫(yī)學(xué)人工智能研究中心，中國科學(xué)院深圳先進(jìn)技術(shù)研究院，廣東 深圳 518055

定量磁共振成像（MRI）可量化組織特性，是科學(xué)研究和臨床研究的重要工具．旋轉(zhuǎn)坐標(biāo)系下的自旋-晶格弛豫時間（1）能反映水與大分子之間的低頻交互作用，在3 T及以上的高場環(huán)境下，1受水和不穩(wěn)定質(zhì)子之間化學(xué)交換的影響較大，通過測量弛豫率隨自旋鎖定場強(qiáng)度的變化而得到其分布情況（1散布），可用于分析和量化質(zhì)子的交換過程，因此1散布是一種重要的定量MRI技術(shù)．然而，獲得不同自旋鎖定場強(qiáng)下1加權(quán)圖像的時間過長，限制了其應(yīng)用范圍．針對這一問題，本研究提出一種基于多弛豫信號補(bǔ)償策略的快速1散布成像方法．該方法將不同鎖定頻率下的1加權(quán)圖像補(bǔ)償?shù)酵恍盘枏?qiáng)度水平，并結(jié)合低秩與稀疏建立重建模型．實驗結(jié)果表明，該方法在加速倍數(shù)高達(dá)7倍時仍獲得了較好的重建結(jié)果．

磁共振定量成像；1散布；信號補(bǔ)償；低秩與稀疏

引 言

磁共振成像（magnetic resonance imaging，MRI）具有無電離輻射、無創(chuàng)傷且對比度豐富等優(yōu)勢，是臨床診斷及療效評估的重要醫(yī)學(xué)影像工具之一．磁共振定量成像是利用MRI技術(shù)量化組織的物理或生理參數(shù)的方法，相較于常規(guī)的結(jié)構(gòu)成像，定量成像在組織間區(qū)分時具有更高的敏感度．定量成像測量的參數(shù)范圍廣泛，不僅包括反映組織物理特性的磁共振弛豫時間（如1、2）和質(zhì)子密度等參數(shù)，還包括反映組織中水分子布朗運(yùn)動、血流灌注等生理特性的擴(kuò)散系數(shù)和灌注分?jǐn)?shù)等[1-5]．

1 基于多弛豫信號補(bǔ)償?shù)腖+S重建原理

1.1 多弛豫信號補(bǔ)償

1.2 L+S重建模型

基于L+S矩陣分解的重建方法已廣泛應(yīng)用于快速磁共振動態(tài)成像中，并取得了較大成功[24-28]．該方法將動態(tài)圖像序列組成的空間-時間矩陣分解為低秩分量矩陣和稀疏分量矩陣的疊加，并通過求解以下凸優(yōu)化問題來進(jìn)行圖像重建：

1.3 基于多弛豫信號補(bǔ)償?shù)腖+S模型

其中，為應(yīng)用于稀疏分量S的全變分變換；為第n個鎖定時間及自旋鎖定頻率下的加權(quán)圖像；d為欠采樣的k空間數(shù)據(jù)；執(zhí)行逐像素的信號補(bǔ)償；，為編碼算子，其中A代表欠采樣算子，F(xiàn)代表傅里葉變換算子，H代表線圈敏感度矩陣[27,29]；代表圖像矩陣的秩．圖1為本文提出的-DISC方法的流程圖．

輸入：d：欠采樣的k空間數(shù)據(jù) E：編碼算子 ：第n個鎖定時間輸出：X：重建圖像1. 初始化和初始定量圖2. 對于外部迭代，執(zhí)行下述步驟直至收斂：[1] 計算[2] [3] 初始化[4] 對于內(nèi)部迭代，執(zhí)行下述步驟：a. 更新，b. 更新，c. 數(shù)據(jù)一致性[5] 內(nèi)部迭代結(jié)束[6] [7] 利用更新[8] 外部迭代結(jié)束

1.4 T1r弛豫模型

在本研究中，我們采用單指數(shù)模型來測量弛豫率：

2 在體實驗

圖2 加速倍數(shù)R分別為(a) 4和(b) 7時，相位編碼-幀方向的欠采樣模板

我們對比了不同方法的計算復(fù)雜度，并以歸一化均方根誤差（normalized root mean square error，nRMSE）、結(jié)構(gòu)相似指數(shù)（structural similarity index，SSIM）[33]、峰值信噪比（peak signal-to-noise ratio，PSNR）[34]為指標(biāo)，對不同加速倍數(shù)下各方法的重建圖像進(jìn)行了定量分析．nRMSE的定義如下：

3 結(jié)果與討論

3.1 不同重建方法的重建性能對比

圖3 R=4和7時，經(jīng)T1r-DISC、L+S和BCS方法重建的T1r加權(quán)圖像及誤差圖（ω=100 Hz，TSL=25 ms）

圖4 R=4和7時，經(jīng)T1r-DISC、L+S和BCS方法重建的T1r加權(quán)圖像及誤差圖（ω=500 Hz，TSL=25 ms）

表1 各加速倍數(shù)下，各方法重建的所有自旋鎖定頻率下T1ρ加權(quán)圖像的nRMSE、PSNR及SSIM的均值±標(biāo)準(zhǔn)差對比

圖5 R=4和R=7時，經(jīng)T1r-DISC、L+S和BCS方法重建得到的R1r定量圖及誤差圖（ω=100 Hz）

圖6 R=4和7時，經(jīng)T1r-DISC、L+S和BCS方法重建得到的R1r定量圖及誤差圖（ω=500 Hz）

3.2 計算復(fù)雜度對比

表2 各算法的計算復(fù)雜度對比

3.3 不同自旋鎖定頻率下R1r的變化規(guī)律

圖7 R=4、5、6、7時，利用T1r-DISC方法的重建圖像擬合計算得到的R1r隨自旋鎖定頻率的變化曲線

3.4 討論

此外，基于深度學(xué)習(xí)的快速MRI方法顯示出巨大的應(yīng)用潛力．基于深度學(xué)習(xí)數(shù)據(jù)驅(qū)動的特性，如果有足夠多的數(shù)據(jù)，深度學(xué)習(xí)方法將顯著提高重建圖像的質(zhì)量．神經(jīng)網(wǎng)絡(luò)還可以用于磁共振多層同時激發(fā)成像，提升重建質(zhì)量[37]．文獻(xiàn)[26]提出了一種基于模型的L+S網(wǎng)絡(luò)的動態(tài)磁共振圖像重建方法，該網(wǎng)絡(luò)使用交替線性化最小化方法來解決低秩和稀疏正則化的優(yōu)化問題，并引入了學(xué)習(xí)奇異值閾值法來保證低秩分量與稀疏分量的分離，最后將迭代步驟展開成正則化參數(shù)可學(xué)習(xí)的網(wǎng)絡(luò).

圖8 R=4和7時，利用T1r-DISC 方法在k空間中心全采樣比例分別為0.05、0.10和0.12時重建的T1r加權(quán)圖像及誤差圖（ω = 200 Hz，TSL = 25 ms）

4 結(jié)論

無

表S1 各方法重建圖像評價指標(biāo)的值結(jié)果

[1] DEONI S C, PETERS T M, RUTT B K. High-resolution1and2mapping of the brain in a clinically acceptable time with DESPOT1 and DESPOT2[J]. Magn Reson Med, 2005, 53(1): 237-241.

[2] GANZETTI M, WENDEROTH N, MANTINI D. Whole brain myelin mapping using1-and2-weighted MR imaging data[J]. Front Hum Neurosci, 2014, 8: 671.

[3] KNIGHT M J, MCCANN B, TSIVOS D, et al. Quantitative2mapping of white matter: applications for ageing and cognitive decline[J]. Phys Med Biol, 2016, 61(15): 5587-5605.

[4] SENER R N. Diffusion MRI: apparent diffusion coefficient (ADC) values in the normal brain and a classification of brain disorders based on ADC values[J]. Comput Med Imaging Graph, 2001, 25(4): 299-326.

[5] TAYLOR A J, SALERNO M, DHARMAKUMAR R, et al.1Mapping: basic techniques and clinical applications[J]. JACC Cardiovasc Imaging, 2016, 9(1): 67-81.

[6] ALI S O, FESSAS P, KAGGIE J D, et al. Evaluation of the sensitivity of1MRI to pH and macromolecular density[J]. Magn Reson Imaging, 2019, 58: 156-161.

[7] WANG Y X, ZHANG Q, LI X, et al.1magnetic resonance: basic physics principles and applications in knee and intervertebral disc imaging[J]. Quant Imaging Med Surg, 2015, 5(6): 858-885.

[8] LI X, WYATT C, RIVOIRE J, et al. Simultaneous acquisition of1and2quantification in knee cartilage: repeatability and diurnal variation[J]. J Magn Reson Imaging, 2014, 39(5): 1287-1293.

[9] WANG Y X, YUAN J. Evaluation of liver fibrosis with1MR imaging[J]. Quant Imaging Med Surg, 2014, 4(3): 152-155.

[10] HARIS M, SINGH A, CAI K, et al.1MRI in Alzheimer’s disease: detection of pathological changes in medial temporal lobe[J]. J Neuroimaging, 2011, 21(2): e86-90.

[11] COBB J G, XIE J, GORE J C. Contributions of chemical exchange to1dispersion in a tissue model[J]. Magn Reson Med, 2011, 66(6): 1563-1571.

[12] COBB J G, XIE J, GORE J C. Contributions of chemical and diffusive exchange to1dispersion[J]. Magn Reson Med, 2013, 69(5): 1357-1366.

[13] LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: the application of compressed sensing for rapid MR imaging[J]. Magn Reson Med, 2007, 58(6): 1182-1195.

[14] BHAVE S, LINGALA S G, JOHNSON C P, et al. Accelerated whole-brain multi-parameter mapping using blind compressed sensing[J]. Magn Reson Med, 2016, 75(3): 1175-1186.

[15] PANDIT P, RIVOIRE J, KING K, et al. Accelerated1acquisition for knee cartilage quantification using compressed sensing and data-driven parallel imaging: a feasibility study[J]. Magn Reson Med, 2016, 75(3): 1256-1261.

[16] KAMESH IYER S, MOON B, HWUANG E, et al. Accelerated free-breathing 3D1cardiovascular magnetic resonance using multicoil compressed sensing[J]. J Cardiovasc Magn R, 2019, 21: 5.

[17] LI Y Y, LI L, LI X S, et al. 3D dynamic MRI with homotopic0minimization rconstruction[J]. Chinese J Magn Reson , 2022, 39(1): 20-32.

李嫣嫣, 李律, 李雪松, 等. 基于同倫0范數(shù)最小化重建的三維動態(tài)磁共振成像[J]. 波譜學(xué)雜志, 2022, 39(1): 20-32.

[18] ZHAN J Y, TU Z R, DU X F, et al. Progresses on low-rank reconstruction for non-uniformly sampled NMR spectra[J]. Chinese J Magn Reson, 2020, 37(3): 255-272.

詹嘉瑩, 涂章仁, 杜曉鳳, 等. 基于低秩矩陣的非均勻采樣NMR波譜重建進(jìn)展[J]. 波譜學(xué)雜志, 2020, 37(3): 255-272.

[19] HALDAR J P, LIANG Z P. Low-rank approximations for dynamic imaging[C]// 2011 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2011: 1052-1055.

[20] JACOB M, MANI M P, YE J C. Structured low-rank algorithms: theory, magnetic resonance applications, and links to machine learning[J]. IEEE Signal Process Mag, 2020, 37(1): 54-68.

[21] ZIBETTI M V W, SHARAFI A, OTAZO R, et al. Accelerating 3D-1mapping of cartilage using compressed sensing with different sparse and low rank models[J]. Magn Reson Med, 2018, 80(4): 1475-1491.

[22] PENG X, YING L, LIU Y Y, et al. Accelerated exponential parameterization of2relaxation with model-driven low rank and sparsity priors (MORASA)[J]. Magn Reson Med, 2016, 76(6): 1865-1878.

[23] ZHU Y J, LIU Y Y, YING L, et al. SCOPE: signal compensation for low-rank plus sparse matrix decomposition for fast parameter mapping[J]. Phys Med Biol, 2018, 63(18): 185009.

[24] BOUWMANS T, SOBRAL A, JAVED S, et al. Decomposition into low-rank plus additive matrices for background/foreground separation: A review for a comparative evaluation with a large-scale dataset[J]. Comput Sci Rev, 2017, 23: 1-71.

[25] ONG F, LUSTIG M. Beyond low rank plus sparse: multiscale low rank matrix decomposition[J]. IEEE J Sel Topics Signal Process, 2016, 10(4): 672-687.

[26] HUANG W Q, KE Z W, CUI Z X, et al. Deep low-rank plus sparse network for dynamic MR imaging[J]. Med Image Anal, 2021, 73.

[27] OTAZO R, CANDES E, SODICKSON D K. Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components[J]. Magn Reson Med, 2015, 73(3): 1125-1136.

[28] PETROV A Y, HERBST M, STENGER V A. Improving temporal resolution in fMRI using a 3D spiral acquisition and low rank plus sparse (L plus S) reconstruction[J]. Neuroimage, 2017, 157: 660-674.

[29] PRUESSMANN K P, WEIGER M, BORNERT P, et al. Advances in sensitivity encoding with arbitrary-space trajectories[J]. Magn Reson Med, 2001, 46(4): 638-651.

[30] MORE J J. The Levenberg-Marquardt algorithm: implementation and theory[J]. Numerical analysis, 1978, 105-116.

[31] MITREA B G, KRAFFT A J, SONG R, et al. Paired self-compensated spin-lock preparation for improved1quantification[J]. J Magn Reson, 2016, 268: 49-57.

[32] RICH A, GREGG M, JIN N, et al. Cartesian sampling with variable density and Adjustable temporal resolution (CAVA)[J]. Magn Reson Med, 2020, 83(6): 2015-2025.

[33] WANG Z, BOVIK A C, SHEIKH H R, et al. Image quality assessment: from error visibility to structural similarity[J]. IEEE Trans Image Process, 2004, 13(4): 600-612.

[34] MASON A, RIOUX J, CLARKE S. Comparison of objective image quality metrics to expert radiologists’ scoring of diagnostic quality of MR Images[J]. IEEE Trans Med Imaging, 2020, 39(4): 1064-1072.

[35] ZHU Y, LIU Y, YING L, et al. A 4-minute solution for submillimeter whole-brain1quantification[J]. Magn Reson Med , 2021, 85(6): 3299-3307.

[36] KORZHNEV D M, OREKHOV V Y, KAY L E. Off-resonance1NMR studies of exchange dynamics in proteins with low spin-lock fields: An application to a fyn SH3 domain[J]. J Am Chem Soc, 2005, 127(2): 713-721.

[37] WANG W T, SU S, JIA S, et al. Reconstruction of simultaneous multi-slice MRI data by combining virtual conjugate coil technology and convolutional neural network[J]. Chinese J Magn Reson, 2020, 37(4): 407-421.

王婉婷, 蘇適, 賈森, 等. 基于虛擬線圈和卷積神經(jīng)網(wǎng)絡(luò)的多層同時激發(fā)圖像重建[J]. 波譜學(xué)雜志, 2020, 37(4): 407-421.

Accelerating1Dispersion Imaging with Multiple Relaxation Signal Compensation

1，1,2，3，3，1，1，1,3，1*

1. Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China; 2. Department of Biomedical Engineering, Chongqing University of Technology, Chongqing 400054, China; 3.Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China

Magnetic resonance imaging (MRI) can quantify characteristic values of tissues, serving as an important tool for scientific and clinical research. Magnetic resonance1relaxation time reflects the low-frequency motional processes between water and macromolecules. At high fields of 3 T and above,1is greatly affected by the chemical exchange between water and exchangeable protons, and1dispersion measured with varying spin-lock fields can be utilized to analyze and quantify the proton exchange process. However, it is time-consuming to obtain1-weighted images with different spin-lock fields, which limits its application. To solve this problem, a fast1dispersion imaging method based on multiple relaxation signal compensation strategy is proposed in this work, which compensates the1-weighted images at different locking frequencies to the same signal strength level, and combines the low-rank plus sparse model in the reconstruction. Experimental results show that the proposed method achieves good reconstruction results even when the acceleration factor is up to 7.

magnetic resonancequantitative imaging,1dispersion, signal compensation,low-rank plus sparse

O482.53

A

10.11938/cjmr20222976

2022-02-16;

2022-04-28

中國科學(xué)院磁共振技術(shù)聯(lián)盟儀器設(shè)備功能開發(fā)技術(shù)創(chuàng)新項目(2020GZL006)；國家重點研發(fā)計劃課題(2020YFA0712200)；廣東省基礎(chǔ)與應(yīng)用基礎(chǔ)研究基金項目(2021A1515110540)；深圳市優(yōu)秀科技創(chuàng)新人才培養(yǎng)項目(RCYX20210609104444089)；中國博士后科學(xué)基金面上項目(2020M682990, 2021M69331, 2021M703390)；廣東省磁共振成像與多模系統(tǒng)重點實驗室(2020B1212060051).

* Tel: 0755-86392243, E-mail: yj.zhu@siat.ac.cn.