Simultaneous Medical Image Fusion and De-Noising with Joint Sparse Representation
1 Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China
2 School of Electrical & Information Engineering, Dalian Jiaotong University, Dalian 116028, Liaoning, China
3 Department of Radiology, the Second Affiliated Hospital of Dalian Medical University, Dalian 116027, Liaoning, China
Abstract：The complementary information of multi-modality medical images can be integrated together, which can provide abundant information and effective help for clinical diagnosis and treatment. Based on the joint sparse model, a new medical image fusion algorithm based on the joint sparse representation was proposed in this paper, and this method could carry out image fusion and de-noising simultaneously while the images were corrupted by noise. First, the registered source images were compiled into column vectors and composed of a joint matrix, and then an over-complete dictionary was obtained through online dictionary learning algorithm(ODL). Second, a joint dictionary was obtained by the over-complete dictionary under the joint sparse model, then based on the joint dictionary, the common sparse coefficients and unique sparse coefficients were computed by the least angle regression algorithm(LARS), and the sparse coefficients of fused image were obtained according to the fusion rule "choose max". Last, the fusion image was reconstructed according to the fusion coefficient and the over-complete dictionary. Compared with three classical algorithms,the results showed that the proposed algorithm has small luminance distortion, small contrast distortion and clear edge texture in the subjective vision, the statistical mean values of the objective parameters MI, QAB/F under noiseless and noisy case were 3.992 3, 2.896 4, 2.505 5 and 0.658, 0.552 4, 0.439 6, respectively. All of these can provide effective help for clinical diagnosis and treatment.
［1］刘兴党．图像融合及其临床应用［J］．国外医学：放射医学核医学分册，1996，20 (4)：156-158．
［2］刘惠，郭冬梅，邱天爽．医学影像和医学图像处理［M］．北京：电子工业出版社，2013：122．
［3］Yang Bin，Li Shutao．Multifocus image fusion and restoration with sparse representation［J］．IEEE Transactions on Instrumentation and Measurement，2010，59(4)：884-892．
［4］Huang W，Jing Z．Evaluation of focus measures in multifocus image fusion［J］．Pattern Recognition Letters，2007，28(4)：493-500．
［5］Nikolov S，Hill P，Bull D，et al．Wavelets for image fusion［M］//Wavelets in Signal and Image Analysis．Amsterdam：Springer Netherlands，2001：213-241．
［6］Das S，Kundu MK．NSCTbased multimodal medical image fusion using pulsecoupled neural network and modified spatial frequency ［J］．Medical & Biological Engineering & Computing，2012，50(10)：1105-1114．
［7］Wang Lei，Li Bin，Tian Lianfang．Multimodal medical image fusion using the interscale and intrascale dependencies between image shiftinvariant shearlet coefficients［J］．Information Fusion，2014，19：20-28．
［8］Mitianoudis N，Stathaki T．Pixelbased and regionbased image fusion schemes using ICA bases［J］．Information Fusion，2007，8(2)： 131-142．
［9］Donoho DL．Compressed sensing［J］．IEEE Transactions on Information Theory，2006，52(4)：1289-1306．
［10］Yu Nannan，Qiu Tianshuang，Bi Feng，et al．Image features extraction and fusion based on joint sparse representation［J］．IEEE Journal of Selected Topics in Signal Processing，2011，5(5)：1074-1082．
［11］Liu Y，Wang Z．Simultaneous image fusion and denoising with adaptive sparse representation［J］．IET Image Processing，2014，9(5)：347-357．
［12］Engan K，Aase S O，Hakon Husoy J．Method of optimal directions for frame design［C］//IEEE Signal Processing Society．Proceedings of the 1999 IEEE International Conference on Acoustics，Speech and Signal Processing(ICASSP
\|99)．Phoenix：IEEE，1999：2443-2446．
［13］Aharon M，Elad M，Bruckstein A．KSVD：An algorithm for designing overcomplete dictionaries for sparse representation［J］．IEEE Transactions on Signal Processing，2006，54(11)：4311-4322．
［14］Mairal J，Bach F，Ponce J，et al．Online dictionary learning for sparse coding［C］//Proceedings of the 26th Annual International Conference on Machine Learning．Montreal：Association for Computing Machinery，2009：689-696．
［15］Efron B，Hastie T，Johnstone I，et al．Least angle regression［J］．The Annals of Statistics，2004，32(2)：407-499．
［16］Mallat SG，Zhang Z．Matching pursuits with timefrequency dictionaries［J］．IEEE Transactions on Signal Processing，1993， 41(12)：3397-3415．
［17］Chen SS，Donoho DL，Saunders MA．Atomic decomposition by basis pursuit［J］．SIAM Journal on Scientific Computing，1998，20(1)：33-61．
［18］Duarte MF，Sarvotham S，Baron D，et al．Distributed compressed sensing of jointly sparse signals［C］//39th Asilomar Conference on Signals, Systems and Computers．Pacific Grove：IEEE Computer Society，2005：1537-1541．
［19］Baron D，Duarte MF，Wakin MB，et al．Distributed compressive sensing［C］//2009 IEEE International Conference on Acoustics，Speech and Signal Processing(ICASSP 2009)．Taipei：IEEE，2009：2886-2889．
［20］Elad M，Aharon M．Image denoising via sparse and redundant representations over learned dictionaries［J］．IEEE Transactions on Image Processing，2006，15(12)：3736-3745．
［21］Xydeas CS，Petrovic V．Objective image fusion performance measure［J］．Electronics Letters，2000，36(4)：308-309．
［22］Qu Guihong，Zhang Dali，Yan Pingfan．Information measure for performance of image fusion［J］．Electronics Letters，2002，38(7)：313-315．
