a Matlab Tool for image restoration with Newton-like Projection methods
NPTool is a software package for image denoising and deblurrig from Gaussian or Poisson corrupted data.
The image formation process is modeled as
The image restoration problem is formulated as the nonnegatively constrained minimization problem
- A is the blurring operator (A is the identity operator in denoising applications)
- bg is the (possible) constant value of the background
- gn is the acquired image corrupted by blur and noise
NPTool is a Matlab implementation of some Newton-like Projection algorithms
for the solution of the previously described constrained optimization problem.
- The data fitting term J0(x) depends on the noise affecting the data:
in the case of Poisson data, J0(x) is the Kullback-Leibler divergence;
in the case of Gaussian data, J0(x) is the Least-Squares term.
- The regularization term JR(x) can be chosen to be the Tikhonov regularization functional (
JR(x)=0.5*||x||^2) or the Total Variation functional.
- Version 1.1, July 2011. The software has been tested on Windows operating system.
The code can be obtained from Netlib (http://www.netlib.org/numeralgo/)
as the na35 package or by clicking here. The code has been developed using Matlab version 7.5.
The Matlab functions are included into a zipped .rar file. Once you have downloaded and unpacked it in your Matlab working directory, type
There is a "Readme" file to guide you in the use of the codes.
The software has been developed by G. Landi and E. Loli Piccolomini.
For any information or comments, please contact landig(at)dm.unibo.it
-  G. Landi, E. Loli Piccolomini. A fast projected quasi-newton method for nonnegative Tikhonov regularization. International Journal of Mathematics and Computer Science 3, 199-213, 2008.
-  G. Landi, E. Loli Piccolomini. A projected Newton-CG method for nonnegative astronomical image deblurring. Numerical Algorithms 48, 279-300, 2008.
-  G. Landi, E. Loli Piccolomini. An improved Newton projection method for
nonnegative deblurring of Poisson-corrupted images with Tikhonov regularization,
Numerical Algorithms, DOI 10.1007/s11075-011-9517-y, 2011.
-  G. Landi, E. Loli Piccolomini. Quasi-Newton projection method for nonnegatively constrained image deblurring, Optimization Online, Applied Mathematics and Computation, 218:2091-2107, 2011.
-  S. Bonettini, G. Landi, E. Loli Piccolomini, L. Zanni. On the scaled gradient projection methods for image deblurring, 2011, submitted.
-  G. Landi, E. Loli Piccolomini. An efficient method for nonnegatively constrained Total-Variation based denoising of medical images corrupted by Poisson noise, Computerized Medical Imaging and Graphics, Vol. 36(1), pp. 38-46, 2012.
This work has been partially supported by the Ministero dell' UniversitÓ e della Ricerca under the Grant number 2006018748.