Recipe to Remove the t₁-noise
Take a column of the processed 2D plot (column = indirect dimension). Use a mapping algorithm to identify the transparent regions (not containing peaks). In the following I'll call them the "noisy regions".
The idea is to delete these region. Setting all their points to zero would be too drastic and unrealistic. What you do, instead, is to calculate the average value in this region. More exactly, the average of the absolute values. At the end you have a positive number which is a measure of the noise along that column. Repeat for all the columns. At the end you have the values of noise for each column. Noise is higher when there is a big peak (on the diagonal or elsewhere). Noise is low where there's no signal. Annotate the minimum value for this noise, let's call it "min". Now, pick again each column. Divide its "noisy regions" by the value of their own noise, then multiply them by "min". The portions containing true peaks are not affected.
The result is that now all the columns show as much noise as the least noisy column. In other words, the noise is = min everywhere.
The merit of this technique is that the final spectrum looks extremely natural, even if it's not. You can't cancel a peak by accident, because nothing has been zeroed.
De-noising, as describe here, can be successfully combined with baseplane correction and symmetrization. Remember that baseplane correction comes first and symmetrization always come last.