How to filter key clicks? I am the author of an amateur radio application that produces a waterfall display across a range of frequencies. Time is on the $x$-axis, frequency is on the $y$-axis, and the relative strength of each signal is depicted by the intensity of color.

Some of the signals have, what are called, "key clicks". That is, at the start and end of each signal, the bandwidth of the signal is wider than the steady-state bandwidth. An example is shown below:

[1] http://www.kkn.net/~n2ic/key_clicks.jpg

These are actually present in the signal - They are not artifacts of my DSP processing. I would appreciate suggestions on how to filter out the key clicks.
Assuming from your screenshot that the frequency magnitudes of "key clicks" are always higher (brighter) than the normal signal, you could just employ a basic Limiter? In other words, if a frequency magnitude value exceeds a certain threshold, set that frequency value to its last (valid) value. If you wanted to keep the plot from looking unnatural, you could simulate the data where the clicks are or use data from previous samples.