NPTool:

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

Ax+bg=gn

where
- 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

min J0(x)+eta*JR(x)

s.t. x>=0

where
s.t. x>=0

- 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

>> startup

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

- [1] 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.
- [2] G. Landi, E. Loli Piccolomini. A projected Newton-CG method for nonnegative astronomical image deblurring. Numerical Algorithms 48, 279-300, 2008.
- [3] 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. - [4] G. Landi, E. Loli Piccolomini. Quasi-Newton projection method for nonnegatively constrained image deblurring, Optimization Online,
*Applied Mathematics and Computation*, 218:2091-2107, 2011. - [5] S. Bonettini, G. Landi, E. Loli Piccolomini, L. Zanni. On the scaled gradient projection methods for image deblurring, 2011, submitted.
- [6] 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' Università e della Ricerca under the Grant number 2006018748.