Some optimization problems seek to minimize a measure on a class of functions. This situation is ubiquitous in signal and image analysis, and in image restoration tasks. Various methods are used when a functional derivative exists.

We have used total variation regularization to improve Abel inversion quality in tomographic applications.

• Abel Inverstion Using Total-Variation Regularization
• Abel Inversion Using Total Variation Regularization: Applications

We have demonstrated signal-dependent noise reduction.

• A Variational Approach to Reconstructing Images Corrupted by Poisson Noise