Skip to main content
SpringerLink
Log in

Image reconstruction based on improved block compressed sensing

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Compressed sensing (CS) technique can sample and compress simultaneously. Since an image contains a huge amount of information, block CS (BCS) technique has appeared. This technique can divide image signals into non-overlapping sub-blocks and all the sub-blocks are processed separately. In classical BCS, translations of coefficients may cause signal losses when constructing sparse matrices. Therefore, reconstructed images are unsatisfactory at low sparsity. In this paper, we propose an improved BCS (IBCS). Our implementation is based on Mallat reconstruction algorithm to construct a non-square sparse matrix, it can retain more information of original signals. The reconstruction quality is more stable at different sparsity. Two experiments demonstrate that the reconstruction quality of the proposed IBCS is better than that of CBCS at lower sparsity and the implementation cost is reduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Baraniuk RG, Davenport M, DeVore RA, Wakin M (2008) A simple proof of the restricted isometry property for random matrices. Construct Approx 28(3):253–263

    Article  MathSciNet  Google Scholar 

  • Bigot J, Boyer C, Weiss P (2016) An analysis of block sampling strategies in compressed sensing. IEEE Trans Inf Theory 62(4):2125–2139

    Article  MathSciNet  Google Scholar 

  • Candès EJ (2006) Compressive sampling. Proc Int Congr Math 3:1433–1452

    MathSciNet  MATH  Google Scholar 

  • Candès EJ, Romberg J (2007) Sparsity and incoherence in compressive sampling. Inverse Probl 23(3):969–985

    Article  MathSciNet  Google Scholar 

  • Candès EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Process Mag 25(2):21–30

    Article  Google Scholar 

  • Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math 41:909–996

    Article  MathSciNet  Google Scholar 

  • Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306

    Article  MathSciNet  Google Scholar 

  • Fannjiang AC, Strohmer T, Yan PC (2010) Compressed remote sensing of sparse objects. Siam J Imaging Sci 3(3):595–618

    Article  MathSciNet  Google Scholar 

  • Gehm ME, John R, Brady DJ, Willett RM, Schulz TJ (2007) Single-shot compressive spectral imaging with a dual-disperser architecture. Opt Express 15(21):14013–14027

    Article  Google Scholar 

  • Haldar JP, Hernando D, Liang ZP (2011) Compressed-sensing MRI with random encoding. IEEE Trans Med Imaging 30(4):893–903

    Article  Google Scholar 

  • Li C, Jiang H, Wilford P, Zhang Y, Scheutzow M (2013) A new compressive video sensing framework for mobile broadcast. IEEE Trans Broadcast 59(1):197–205

    Article  Google Scholar 

  • Lima LH, Comon P (2010) Multiarray signal processing: tensor decomposition meets compressed sensing. Comptes Rendus Mecanique 338(6):311–320

    Article  Google Scholar 

  • Lustig M, Donoho DL, Santos JM, Pauly JM (2008) Compressed sensing MRI. IEEE Signal Process Mag 25(2):72–82

    Article  Google Scholar 

  • Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11:674–693

    Article  Google Scholar 

  • Mallat SG (1989) Multiresolution approximations and wavelet orthonormal bases of L2. Trans Am Math Soc 315(1):69–87

    MATH  Google Scholar 

  • Noschese S, Reichel L (2011) The structured distance to normality of Toeplitz matrices with application to preconditioning. Numer Linear Algebra Appl 18(3):429–447

    Article  MathSciNet  Google Scholar 

  • Pudlewski S, Melodia T, Prasanna A (2012) Compressed-sensing-enabled video streaming for wireless multimedia sensor networks. IEEE Trans Mob Comput 11(6):1060–1072

    Article  Google Scholar 

  • Sahoo SK, Makur A (2015) Signal recovery from random measurements via extended orthogonal matching pursuit. IEEE Trans Signal Process 63(10):2572–2581

    Article  MathSciNet  Google Scholar 

  • Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666

    Article  MathSciNet  Google Scholar 

  • Vu VT, Pettersson MI (2015) Nyquist sampling requirements for polar grids in bistatic time-domain algorithms. IEEE Trans Signal Process 63(2):457–465

    Article  MathSciNet  Google Scholar 

  • Wei JB, Huang YK, Lu K, Wang LZ (2016) Nonlocal low-rank-based compressed sensing for remote sensing image reconstruction. IEEE Geosci Remote Sens Lett 13(10):1557–1561

    Article  Google Scholar 

  • Zhou Y, Guo HN (2019) Collaborative block compressed sensing reconstruction with dual-domain sparse representation. Inf Sci 472:77–93

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, 524088, China

    Hong Du & Huixian Lin

Authors
  1. Hong Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huixian Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huixian Lin.

Additional information

Communicated by Eduardo Souza de Cursi.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, H., Lin, H. Image reconstruction based on improved block compressed sensing. Comp. Appl. Math. 41, 4 (2022). https://doi.org/10.1007/s40314-021-01706-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-021-01706-0

Keywords

Search

Navigation