<p>I am new, so may have a biased sample, but it seems a lot of the discussion on "regularized regression" focuses on methods that penalize some norm of the parameter (coefficient) vector. For example in this context <a href="https://stats.stackexchange.com/tags/ridge-regression/info">ridge regression</a> is the $L_2$ variant and <a href="https://stats.stackexchange.com/tags/lasso/info">LASSO</a> is the $L_1$ variant.</p>

<p>However in my experience* <a href="https://en.wikipedia.org/wiki/Tikhonov_regularization" rel="nofollow noreferrer">Tikhonov regularization</a> is typically considered a superset of ridge regression rather than a <a href="https://stats.stackexchange.com/tags/ridge-regression/synonyms">synonym</a>. (*mostly geophysics inverse problems.) The usage I usually hear is more in line with the Wikipedia definition (linked above), where essentially any matrix can be used on the regularization term, i.e. not just the identity. For example a spatial derivative operator is commonly used in geophysics and computational photography, where the parameter vector represents <a href="https://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit" rel="nofollow noreferrer">gridded data</a>. (This usage also seems to be consistent with Richard Szeliski's well-known <a href="https://scholar.google.com/scholar?cluster=16605107453260999726" rel="nofollow noreferrer">Computer Vision textbook</a>.)</p>

<p>Is there another term that would be used for this generalized form of in statistics/machine learning? Is it just considered a special case of MAP estimation for correlated Gaussian errors?</p>
