compressive sensing says while capturing a signal take random measurements of signal using random matrices (gaussian etc.) and while reconstructing the signal at reciever we use sparsifying basis but some researchers perform sparsification after capturing the signal and then take random measurements of this sparsified signal using random matrices but performing sparisification at the encoder/transmitter is it a correct way
Both are correct. The first approach is common Compressive sensing. The second approach give you a chance to utilize structure of signal in sparsify domain. For example, the low frequency is often more important than the high frequency (as human visual system is more sensitive to low-frequency in image processing application). The second approach often refers to hybrid compressive sensing, multi scale compressive sensing which also discussed in very beginning time of CS.
I forgot to attack the paper. It was also written by Donoho
http://www.sciencedirect.com/science/article/pii/S0165168405002215
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