A quasi-Newton projection method for nonnegatively constrained image deblurring
نویسندگان
چکیده
In this paper we present a quasi-Newton projection method for image deblurring. The mathematical problem is a constrained minimization problem, where the objective function is a regularization function and the constraint is the positivity of the solution. The regularization function is a sum of the Kullback-Leibler divergence, used to minimize the error in the presence of Poisson noise, and of a Tikhonov term. The Hessian of the regularization function is approximated in order to invert it using Fast Fourier Transforms. The numerical experiments on some astronomical images blurred by simulated Point Spread Functions show that the method gives very good results both in terms of relative error and computational efficiency.
منابع مشابه
Quasi-newton Approach to Nonnegative Image Restorations
Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform based schemes result in eecient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an ima...
متن کاملQuasi - Newton Approach to Nonnegative
Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform based schemes result in eecient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an ima...
متن کاملRegularizing active set method for nonnegatively constrained ill-posed multichannel image restoration problem.
In this paper, we consider the nonnegatively constrained multichannel image deblurring problem and propose regularizing active set methods for numerical restoration. For image deblurring problems, it is reasonable to solve a regularizing model with nonnegativity constraints because of the physical meaning of the image. We consider a general regularizing l(p)-l(q) model with nonnegativity constr...
متن کاملA limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction.
Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variab...
متن کاملTotal variation-penalized Poisson likelihood estimation for ill-posed problems
The noise contained in data measured by imaging instruments is often primarily of Poisson type. This motivates, in many cases, the use of the Poisson likelihood functional in place of the ubiquitous least squares data fidelity when solving image deblurring problems. We assume that the underlying blurring operator is compact, so that, as in the least squares case, the resulting minimization prob...
متن کامل