A MULTIPLICATIVE ITERATIVE ALGORITHM FOR BOX-CONSTRAINED PENALIZED LIKELIHOOD IMAGE RESTORATION
A MULTIPLICATIVE ITERATIVE ALGORITHM FOR BOX-CONSTRAINED PENALIZED LIKELIHOOD IMAGE RESTORATION
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 pixel wise 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.
Existing System:
A Most of these methods have the following two major weaknesses:
1) they mostly consider the Gaussian noise (equivalently least-squares restoration) and
2) they are developed based on gradient projection algorithms, which can be either slow converging or require identification of the active sets in every iteration.
Identifying the active set in each iteration can be a significant computational burden for image processing. In contrast, the method developed in this paper completely avoids active sets and is remarkably easy to implement
Proposed System:
The penalty function (equivalent to the negative log prior density function in the context of MAP) is used to restrict the restored image, such that it satisfies certain local smoothness conditions. The box-constrained problem is solved by an MI algorithm extended from the MI algorithm, which has been successfully applied to positively constrain tomographic reconstruction. This new MI algorithm can handle a general noise distribution such as Gaussian, Poisson, and Laplace and any penalty function as long as its first derivative is available, making it feasible for many well-known penalty functions in image processing. Note that, however, for some edge-preserving penalties, such as the total variation (TV) and Gaussian–Markov random field penalties.
Software Requirements:
.Net
Front End – ASP.Net
Language – C#.Net
Back End – SQL Server
Windows XP
Hardware Requirements:
RAM : 512 Mb
Hard Disk : 80 Gb
Processor : Pentium IV
FUTURE ENHANCEMENT:
We comments that research on other box-constrained optimization methods for large-scale problems, such as the conjugate gradient algorithm and the spectral projected gradient algorithm, may be also useful for image deblurring and denoising with box constraints. However, it requires further assessments to confirm the effectiveness of these algorithms.
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