Cook linguine according to package directions. Meanwhile, in a skillet, saute onions and garlic in oil until tender. Add mushrooms and tomatoes; cook and stir for 3 minutes. Stir in the artichoke hearts, wine or broth, Italian seasoning, salt, rosemary and pepper. Bring to a boil. Reduce heat; simmer, uncovered, for 5 minutes or until mixture reaches desired thickness.
Add shrimp; cook and stir for 3 minutes or until shrimp turn pink. Drain linguine; top with shrimp mixture and toss to coat. Sprinkle with Parmesan cheese if desired.