Golay sequence for parital Fourier and Hadamard compressive imaging

This paper introduces Golay sequence for partial Fourier and Hadamard compressive imaging. In the proposed system, the signal is pre-modulated by a binary Golay sequence before applying a random subsampled Fourier or Hadamard transform. The correpsonding sampling operator has been proved to be incoherent with the (block) DCT or the Haar wavelet transform. Empirical results show that they are also incoherent with the Daubechies wavelets. It is well known that natural images are sparse in the DCT and the wavelet basis. Hence, the proposed sampling operators are promising in many Fourier or Hadamard compressive imaging applications. In fact, they can achieve near-optimal reconstruction performance with small memory requirement and simple hardware implementation. Some simulation results and proof-of-concept experimental results are included to demonstrate the validity of the theory and the potential of the proposed sampling operators.