Detection of a Pulse pattern with Matched filter
IF a 1 is always represented by the waveform in the figure, you can use that waveform as the matched filter response.
However, it sounds like the waveform could be anything as long as there are some pulses in it. In that case, the matched filter should be a single pulse, and you'll have to count how many pulses were detected afterwards.
The non-Gaussian noise can be a problem; if you don't know anything about its distribution, you'll probably just have to build a prototype and test it. You may end up having to design a filter tailored to the specific noise distribution in your system.