The technical content of a patent is public information.
You intend to publish your improvements which does not constitute patent infringement. For an infringing action, you would have to do more than that.
Third parties might be inspired to unknowingly infringe on the original patent by monetizing your ideas (the improved invention). That is generally not your responsibility; if you provide appropriate references to any applicable patent protection known to you, that's the ethical thing to do, but not a requirement of patent law.
If you, on the other hand, decide to monetize your own improvement, or anything else that embodies the original patented idea (improved or not), you are infringing regardless of how carefully you handle citations, unless you procured a specific license from the patent holder.
The exact line between just "advertising" (the potential commercial value of) somebody else's invention and indirect infringement (e.g., by licensing an implementation of a software component that can easily be used in infringing ways and cannot be used in any non-infringing ways, and/or by inducing actual 3rd party use thereof somehow) can be jurisdiction dependent. Indirect infringement generally requires intent that an actual infringement by a third party would eventually happen, and a bona fide academic publication has demonstrably entirely different (publisher's and author's) goals. If you think that a patent holder could hate your publication enough to sue you for indirect infringement, ask yourself what would make them see it as a blatant infringement tool rather than a welcome advertisement of their undisputed ownership and see whether you can make your academic intents even clearer in how you report on your research results.
(When citing patents, remember that their existence and content proves that somebody owns a certain idea, but not that all the technical details, or even the entire idea behind the patent, is scientifically sound. This means that patents tend to be referenced for different purposes than prior research would be.)