The sampling system based on Gabor frames with exponential reproducing windows holds nice performance for short pulses in general cases, but when the frames are highly redundant, the traditional coefficient oriented methods for subspace detection may fail or have large error. Firstly, the signal oriented idea is introduced and the blocked dual Gabor dictionaries are constructed, finishing the block sparse representation. By introducing the blocked dictionaries, the measurement matrix is constructed and the block ε-coherence restricted by the coherence of the dictionaries is proposed. Consequently, the synthesis model for signal representation is introduced to subspace detection based on Multiple Measurement Vector problem and the Simultaneous Orthogonal Matching Pursuit is proposed based on blocked ε-closure(SOMP_Bε,F), using for subspace detection. Additionally, the convergence of the algorithm is proved. At last, simulation experiments prove that the new method improves the recovery rate, decreases the channel numbers and enforces the robustness of the sampling system compared with the traditional methods.