A multiplicative iterative algorithm for box-constrained penalized likelihood image restoration

Raymond H. Chan*, Jun Ma

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)


    Image restoration is a computationally intensive problem as a large number of pixel values have to be determined. Since the pixel values of digital images can attain only a finite number of values (e.g., 8-bit images can have only 256 gray levels), one would like to recover an image within some dynamic range. This leads to the imposition of box constraints on the pixel values. The traditional gradient projection methods for constrained optimization can be used to impose box constraints, but they may suffer from either slow convergence or repeated searching for active sets in each iteration. In this paper, we develop a new box-constrained multiplicative iterative (BCMI) algorithm for box-constrained image restoration. The BCMI algorithm just requires pixelwise updates in each iteration, and there is no need to invert any matrices. We give the convergence proof of this algorithm and apply it to total variation image restoration problems, where the observed blurry images contain Poisson, Gaussian, or salt-and-pepper noises.

    Original languageEnglish
    Article number6156784
    Pages (from-to)3168-3181
    Number of pages14
    JournalIEEE Transactions on Image Processing
    Issue number7
    Publication statusPublished - Jul 2012

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