How to deal with random spikes in data?

I'm reading really noisy data, with a few anomalies. I'm using SIMULINK and using different filters to get rid of the anomalies, however i get a really bad lag time.

I'm not too worried about the noise right now just getting rid of the anomalies at this moment. I'm thinking of adding a memory block to somehow read the previous value and if it spikes a certain percentage just to hold the previous value, extrapolate a value.

How would I go about doing this, any suggestions?

[Di]

I would really like to know as well