Reconstruct the compressively sensed complex-valued terahertz data through BFGS method

In this paper, we present a new algorithm to reconstruct the compressively sensed complex-valued terahertz data by solving a ℓ₁-norm minimization problem. The approach is based on an improved quasi-Newton algorithm. We use the discrete cosine transform and discrete wavelet transform respectively as the sparsity-promotion basis for the complex-value data. Application of the proposed method to both synthetic and real THz data shows that the proposed method achieves better performance compared to the existing methods.