Proposed changes

Significantly simplifies the code and makes it easier to modify the different reconstruction schemes simultaneously.

Upgrade instructions

Code review checklist

• The code is documented and the documentation renders correctly. Run
  make doc to generate the documentation locally into BUILD_DIR/docs/html.
  Then open index.html.
• The code follows the stylistic and code quality guidelines listed in the
  code review guide.
• The PR lists upgrade instructions and is labeled bugfix or
  new feature if appropriate.

Further comments