A family of measurement basis for fast compressed imaging

Abstract

With the advent of a single-pixel camera, compressed imaging has gained wide interests. However, the design of efficient measurement basis in such a system remains a challenging problem. In order to achieve fast and accurate compressed imaging, we propose a special family of measurement matrices, according to the coefficients distribution characteristics of natural images in sparse domain. The measurement matrix which can precisely locate the position of zero or approximate zero coefficients significantly outperforms the commonly used random matrix. And combining with the specific blocking strategy, the reconstruction speed can be increased linearly and the reconstruction performance is almost unchanged. Moreover, there is no blocking artifact. Several numerical experiments verify the validity of the measurement matrix. All image blocks are completely independent, so parallel fast compressed imaging could be realized.

References

[1] ShinJ., BosworthB. T., FosterM. A.. Optics Letters, 2016, 41: 886

[2] MarciaR.F., KimC., KimJ., BradyD.J., WillettR.M.. Fast Disambiguation of Superimposed Images for Increased Field of View, IEEE International Conference on Image Processing, 2620, 2008,

[3] KoppalS. J., GkioulekasI., YoungT.. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2013, 35: 2982

[4] GehmM. E., JohnR., BradyD. J., WillettR. M., SchultzT. J.. Opt. Express, 2007, 15: 14013

[5] WagadarikarA., JohnR., WillettR., BradyD.. Appl. Opt. 47, B44, 2008,

[6] ClariceP.. Applied & Computational Harmonic Analysis, 2015, 32: 193

[7] SoltanolkotabiM.. Structured Signal Recovery from Quadratic Measurements: Breaking Sample Complexity Barriers via Non-Convex Optimization, 2017,

[8] ChenG. H., TangJ.. Method for Constrained Reconstruction of High Signal-to-noise Ratio Images: US, 2014,

[9] A Sarıduman, AE Pusane and ZC Taşkın, A Heuristic Method for Adaptive Linear Programming Decoding, Signal Processing & Communication Application Conference, 1665 (2016).

[10] L. Gan, Block Compressed Sensing of Natural Images, IEEE Xplore Conference: Digital Signal Processing, 403 (2007).

[11] YangY., AuO.C., FangL., WenX., TangW.. Perceptual Compressive Sensing for Image Signals, IEEE International Conference on Multimedia and Expo, 89, 2009,

[12] P Sermwuthisarn, S Auethavekiat and V Patanavijit, A Fast Image Recovery Using Compressive Sensing Technique with Block Based Orthogonal Matching Pursuit, ISPACS, 212 (2009).

[13] Manotas GutiérrezI., Arguello FuentesH.. Revista Facultad de Ingenieria, 2014,

[14] RHS., TS.. Optical Engineering, 2017, 56: 0413

[15] RachlinY., ShahV.. RH Shepard and T Shih, Dynamic Optically Multiplexed Imaging, Image Reconstruction from Incomplete Data VIII, International Society for Optics and Photonics, 2015,

[16] FlorianP.. Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems, 114, 2008,

[17] KlerkE.D., VallentinF.. Mathematics, 2016, 26: 1944

[18] CandesE., RombergJ.. Inverse Problems, 2007, 23: 969