Do you want to decompose the given tensor with the constraint that each element of the resulting TT-tensor should be non-negative, or that the TT-cores are non-negative (the later implies the former, but not vice versa)?
In both cases this is non-trivial and there is no analytical solution (e.g. you can't do that with a few SVDs), but you can pose an optimization problem to approximate the answer.
Do you want to decompose the given tensor with the constraint that each element of the resulting TT-tensor should be non-negative, or that the TT-cores are non-negative (the later implies the former, but not vice versa)?
In both cases this is non-trivial and there is no analytical solution (e.g. you can't do that with a few SVDs), but you can pose an optimization problem to approximate the answer.