It is widely known that the family of projection filters includes the generalized inverse filter, and that the family of parametric projection filters includes parametric generalized projection filters. However, relations between the family of parametric projection filters and constrained least squares filters are not sufficiently clarified. In this paper, we consider relations between parameter estimation and image restoration by these families. As a result, we show that the restored image by the family of parametric projection filters is a maximum penalized likelihood estimator, and that it agrees with the restored image by constrained least squares filter under some suitable conditions.