I am looking for a tutorial on Tikhonov matrix, in the sense what it can do or it cannot do. The definition of the matrix can be obtained in the wikipedia link. https://en.wikipedia.org/wiki/Tikhonov_regularization I understand the $L_2$ regularization mentioned in the link, but I am interested to choose function which favors ramp like behavior (not low norm), in a way I want to compensate for attenuation of signals. Is it possible? Any comments would be appreciated.
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$\begingroup$ Since your question seems to be mostly concerned with modeling, it would be more suitable for the Signal Processing Stackexchange, dsp.stackexchange.com. But briefly: you shouldn't look only at the matrix, but the whole term including the squared norm. If you wish to favor piecewise affine signals (I assume this is what you mean by "ramp like"), you should consider "total generalized variation" as a penalty. $\endgroup$– Christian ClasonCommented Sep 16, 2016 at 11:36
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$\begingroup$ @ChristianClason Thank you for your interest. The signals are highly attenuated, so, it is a kind of special case. Looking to ignore early reflections with ramp like regularization. $\endgroup$– lordOfTheRingsCommented Sep 16, 2016 at 19:38
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