aptitude supports searching among all packages known to the package management tools, installed or otherwise, using regular expressions, without extraneous output, and can be told how to format its output:
aptitude search "linux-image-.*"
To list only installed packages:
aptitude search "linux-image-.* ~i"
To list only installed package names matching the regular expression:
aptitude search "linux-image-.* ~i" -F "%p"
The documentation covers the available search patterns and output format specifiers in detail. You’ll also find examples on this site, for example is there a way to use regexp with aptitude?, regexp with aptitude part 2, and Linux - display or upgrade security updates only using apt.