Analysis of radially restored images for spherical single lens cellphone camera

Yupeng Zhang*, Ikumi Minema, Lev G. Zimin, Toshitsugu Ueda

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)


    A spherical single lens imaging system for cellphone camera is proposed in this research. The overall thickness from the front surface of the lens to the image sensor is approximately 4.5 mm, which is competitive compared to 6~7 mm of current cellphone camera modules that use compound lens system. One defect of this spherical single lens that deteriorates image quality is radially variant blur, which is produced by one of the optical aberrations called field curvature. We describe a novel method of blur restoration that employs polar image and polar Point Spread Function (PSF) converted from Cartesian image and Cartesian PSF. The blurred image was radially segmented into several regions, to which polar PSFs at different field angles were applied. Results of visual and quantitative evaluation indicate that number of segmented regions and weighted average of β / n$ ratios, i.e., ratio of bandwidth to the number Circulant Blocks (CBs) of the polar PSF Block-Toeplitz-with-Circulant-Blocks (BTCB) matrices affect the restored image quality and Mean Square Error (MSE). Evaluation results on restored images using different polar image resolutions revealed that high resolution obtains good pixel continuity, whereas low resolution results in radially expanding pixel vacancies.

    Original languageEnglish
    Article number6015526
    Pages (from-to)2834-2844
    Number of pages11
    JournalIEEE Sensors Journal
    Issue number11
    Publication statusPublished - 2011


    • Cellphone cameras
    • image restoration
    • radially variant blur
    • spherical single lens

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Instrumentation


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