Fast nonnegative least squares through flexible Krylov subspaces
This work addresses the need for faster solvers for nonnegative least squares problems in image reconstruction, offering a practical speedup over existing methods.
The paper proposes a new efficient method for nonnegative linear least squares problems by leveraging KKT conditions to form an adaptively preconditioned linear system solved via a flexible Krylov subspace method. The method achieves equal or better solution quality than state-of-the-art methods with significant speedup in image reconstruction tasks.
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares problems. The associated KKT conditions are leveraged to form an adaptively preconditioned linear system, which is then solved by a flexible Krylov subspace method. The new method can be easily applied to image reconstruction problems affected by both Gaussian and Poisson noise, where the components of the solution represent nonnegative intensities. {Theoretical insight is given, and} numerical experiments and comparisons are displayed in order to validate the new method, which delivers results of equal or better quality than many state-of-the-art methods for nonnegative least squares solvers, with a significant speedup.