Multimedia Tools and Applications

, Volume 75, Issue 11, pp 6189–6205 | Cite as

High-quality image restoration from partial mixed adaptive-random measurements

  • Jun Yang
  • Wei E. I. Sha
  • Hongyang Chao
  • Zhu Jin


A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes adaptive edge measurements extracted from a low-resolution image with uniform random measurements predefined for the high-resolution image to be recovered. The mixed sensing matrix seamlessly captures important information of an image, and meanwhile approximately satisfies the restricted isometry property. To recover the high-resolution image from MAR measurements, the total variation algorithm based on the compressive sensing theory is employed for solving the Lagrangian regularization problem. Both peak signal-to-noise ratio and structural similarity results demonstrate the MAR sensing framework shows much better recovery performance than the completely random sensing one. The work is particularly helpful for high-performance and lost-cost data acquisition.


Data acquisition Mixed adaptive-random sampling Total variation Compressive sensing 



Dr. Sha acknowledges Ms. Qing Ye to motivate the compressive sensing work. We also would like to acknowledge the support of China NSF under Grant 61173081 and 61201122; and Guangdong Natural Science Foundation, China, under Grant S2011020001215.


  1. 1.
    Alliney S, Ruzinsky S (1994) An algorithm for the minimization of mixed l 1 and l 2 norms with application to bayesian estimation. IEEE Trans Sig Process 42(3):618–627CrossRefGoogle Scholar
  2. 2.
    Baraniuk R, Davenport M, DeVore R, Wakin M (2008) A simple proof of the restricted isometry property for random matrices. Constr Approx 28(3):253–263MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Candes EJ, Tao T (2005) Decoding by linear programming. Inf Theory, IEEE Trans on 51(12):4203–4215MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Candes EJ, Tao T (2006) Near-optimal signal recovery from random projections: universal encoding strategies IEEE Trans Inf Theory 52(12):5406–5425MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intel PAMI 8(6):679–698CrossRefGoogle Scholar
  7. 7.
    Dai QI , Sha WEI (2009) The physics of compressive sensing and the gradient-based recoveryalgorithms. ArXiv:0906.1487
  8. 8.
    Dai W, Milenkovic O (2009) Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans Inf Theory 55(5):2230–2249MathSciNetCrossRefGoogle Scholar
  9. 9.
    Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communs Pure Appl Math 57 (11):1413–1457MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Do TT, Gan L, Nguyen NH , Tran TD (2012) Fast and efficient compressive sensing using structurally random matrices. IEEE Trans Signal Process 60 (1):139–154MathSciNetCrossRefGoogle Scholar
  11. 11.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Donoho DL, Tsaig Y, Drori I, Starck JL (2012) Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans Inf Theory 58(2):1094–1121MathSciNetCrossRefGoogle Scholar
  13. 13.
    Figueiredo MA, Nowak RD, Wright SJ (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. Selected Topics in Signal Process, IEEE J 1 (4):586–597CrossRefGoogle Scholar
  14. 14.
    Hager WW, Zhang H (2006) A survey of nonlinear conjugate gradient methods. Pac J Optim 2(1):35–58MathSciNetMATHGoogle Scholar
  15. 15.
    Hale ET, Yin W, Zhang Y (2008) Fixed-point continuation for 1-minimization: methodology and convergence. SIAM J Optim 19(3):1107–1130MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Keys R (1981) Cubic convolution interpolation for digital image processing. IEEE Trans Acoustics, Speech and Signal Process 29(6):1153–1160MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Li P, Hastie TJ, Church KW (2006) Very sparse random projections. In: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 287–296. ACMGoogle Scholar
  18. 18.
    Lustig M, Donoho D, Pauly JM (2007) Sparse mri: the application of compressed sensing for rapid mr imaging. Magn Reson Med 58(6):1182–1195CrossRefGoogle Scholar
  19. 19.
    Needell D, Ward R (2013) Stable image reconstruction using total variation minimization. SIAM J Imaging Scie 6(2):1035–1058MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Osher S, Solé A, Vese L (2003) Image decomposition and restoration using total variation minimization and the h −1 norm. Multiscale Modeling Simul 1(3):349–370MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Parker JR (1997) Algorithms for Image Processing and Computer Vision. John Wiley & Sons, Inc., New YorkGoogle Scholar
  22. 22.
    Romberg J (2007) Sensing by random convolution. In: Computational Advances in Multi-Sensor Adaptive Processing, 2007. CAMPSAP 2007. 2nd IEEE International Workshop on, pp. 137–140. IEEEGoogle Scholar
  23. 23.
    Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenom 60(1):259–268MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Van Den Berg E, Friedlander MP (2008) Probing the pareto frontier for basis pursuit solutions. SIAM J Sci Comput 31(2):890–912MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Zhang J, Xiong R, Ma S, Zhao D (2011) High-quality image restoration from partial random samples in spatial domain. In: VCIP’11, pp. 1–4Google Scholar
  27. 27.
    Zhang J, Zhao D, Gao W (2014) Group-based sparse representation for image restorationGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Information Science and TechnologySun Yat-sen UniversityGuangzhouChina
  2. 2.Department of Electrical and Electronic EngineeringThe University of Hong KongPokfulam RoadHong Kong
  3. 3.School of SoftwareSun Yat-sen UniversityGuangzhouChina

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