In a large pan, combine the asparagus with 1/2 cup of water and bring it to a boil. Reduce the heat and simmer, until the asparagus is tender but crisp, about 6 minutes. Drain and run cold water to cool and stop the cooking process; pat dry to prevent a watery dip. In a food processor, pulse the asparagus, cilantro, garlic, lime juice and salt. Pulse until the dip is the consistency you desire. Gently stir in chunky salsa, drained of liquid, and transfer to a serving bowl. Cover and refrigerate, until chilled, about 1 hour.