The bandwidth upgrade required in short-reach optical communications has prompted the need for detection schemes that combine field reconstruction with a cost-effective subsystem architecture. Here we propose an asymmetric self-coherent detection (ASCD) scheme for the field reconstruction of self-coherent (SC) complex double-sideband (DSB) signals based on a direct-detection (DD) receiver with two reception paths. Each reception path consists of a photodiode (PD) and an analog-to-digital converter for the detection of a part of the received optical signal that experiences a different optical transfer function via the configuration of an optical filter. We derive an analytical solution to reconstructing the signal field and show the optimal filter response in optimizing the signal SNR. Further, we numerically characterize the theoretical performance of a specific ASCD scheme based on a chromatic dispersion filter and validate the principle of the ASCD scheme in a proof-of-concept experiment. The ASCD scheme approaches the electrical spectral efficiency of coherent detection with a cost-effective DD receiver, which shows the potential for high-speed short-reach links required by edge cloud communications and mobile X-haul systems.