Reconstruction of a complex-valued object without a support constraint

This study demonstrates that a nonnegative complex-valued object without support constraints can be reconstructed from its diffraction pattern, even with partially missing data. We employed a continuous hybrid input-output (CHIO) algorithm, which imposes double nonnegative constraints on the real and imaginary parts of the object. The missing data at the diffraction pattern center is recovered linearly before iterations. Simulations and experiments indicate that this method yields more accurate results and lower reconstruction errors than the hybrid input-output (HIO) algorithm, thus offering a robust approach for coherent diffraction microscopy of biological samples using soft x rays or visible light lasers.