  In this work, we study resolvent splitting algorithms for solving composite
monotone inclusion problems. The objective of these general problems is finding
a zero in the sum of maximally monotone operators composed with linear
operators. Our main contribution is establishing the first primal-dual
splitting algorithm for composite monotone inclusions with minimal lifting.
Specifically, the proposed scheme reduces the dimension of the product space
where the underlying fixed point operator is defined, in comparison to other
algorithms, without requiring additional evaluations of the resolvent
operators. We prove the convergence of this new algorithm and analyze its
performance in a problem arising in image deblurring and denoising. This work
also contributes to the theory of resolvent splitting algorithms by extending
the minimal lifting theorem recently proved by Malitsky and Tam to schemes with
resolvent parameters.
