Reconstruction of compressively sensed complex-valued terahertz data

Traditionally, compressed sensing (CS) has been presented considering real-valued data. There has been some recent interest in reconstruction algorithms for CS that can handle and take advantage of complex-valued data. This kind of data is common in terahertz (THz) imaging. CS reconstruction in such a case can benefit from extra information provided by phase or real and imaginary parts of the data. In this paper, we present an algorithm based on iterative shrinkage/thesholding that takes into account this extra information for reconstruction of compressively sensed complex-valued data. We use curvelets as sparsity-promoting basis for real and imaginary parts of THz data and show using actual THz data that reconstruction performance is improved. Moreover, compared to existing methods, the proposed method is computationally efficient, flexible and suitable for large-size data.