Variational deconvolution of multi-channel images with inequality constraints \

A constrained variational deconvolution approach for multi-channel images is presented. Constraints are enforced through a reparametrisation which allows a differential geometric reinterpretation. This view point is used to show that the deconvolution problem can be formulated as a standard gradient descent problem with an underlying metric that depends on the imposed constraints. Examples are given for bound constrained colour image deblurring, and for diffusion tensor magnetic resonance imaging with positive definiteness constraint. Numerical results illustrate the effectiveness of the methods.