A multiplicative regularization approach for deblurring problems

• Published in: IEEE transactions on image processing 2004-11, Vol.13 (11), p.1524-1532
• Main Authors: Abubakar, A., van den Berg, P.M., Habashy, T.M., Braunisch, H.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Blurring; Character generation; Cluster Analysis; Computer Graphics; Computer Simulation; Deconvolution; Electromagnetic scattering; Errors; Exact sciences and technology; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image reconstruction; Imaging, Three-Dimensional - methods; Information Storage and Retrieval - methods; Information, signal and communications theory; Inverse problems; Iterative algorithms; Iterative methods; Linearity; Mathematical models; Noise; Numerical Analysis, Computer-Assisted; Operators; Pattern Recognition, Automated - methods; Regularization; Reproducibility of Results; Sensitivity and Specificity; Signal processing; Signal Processing, Computer-Assisted; Studies; Subtraction Technique; Telecommunications and information theory; Testing
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2004.836172

In this work, an iterative inversion algorithm for deblurring and deconvolution is considered. The algorithm is based on the conjugate gradient scheme and uses the so-called weighted L/sub 2/-norm regularizer to obtain a reliable solution. The regularizer is included as a multiplicative constraint. In this way, the appropriate regularization parameter will be controlled by the optimization process itself. In fact, the misfit in the error in the space of the blurring operator is the regularization parameter. Then, no a priori knowledge on the blurred data or image is needed. If noise is present, the misfit in the error consisting of the blurring operator will remain at a large value during the optimization process; therefore, the weight of the regularization factor will be more significant. Hence, the noise will, at all times, be suppressed in the reconstruction process. Although one may argue that, by including the regularization factor as a multiplicative constraint, the linearity of the problem has been lost, careful analysis shows that, under certain restrictions, no new local minima are introduced. Numerical testing shows that the proposed algorithm works effectively and efficiently in various practical applications.