## 1 Introduction  
Stereo loudspeaker reproduction is widely used to provide a more natural listening experience because of the distinguished relative positions of objects and events in the horizontal plane [1]. In fact, a stereo audio system can deliver a more immersive illusion than a mono system, because spatial information (e.g., inter-channel time difference (ICTD) and inter-channel level difference (ICLD) [2]) helps listeners perceive a horizontal direction [3]. In addition, according to duplex theory [2], the ICTD and ICLD are dominant for horizontal sound localization at low frequencies (below 1-2 kHz) and high frequencies (above 1-2 kHz), respectively. Stereo audio recording techniques can be classified into three different categories depending on the placement and characteristics of microphones: coincident, near-coincident, and spaced recording techniques [4; 5]. Coincident recording techniques such as the XY and mid-side (MS) techniques [5] place stereo microphones as close together as possible at different angles to capture a stereophonic image, where the stereophonic image is about sound recording and reproduction concerning the perceived spatial locations of the sound source. Thus, a good stereophonic image means that the location of the sound source can be clearly perceived, while a poor one means that the location of the source is difficult to be perceived [6]. In addition, near-coincident recording techniques such as the Office de Radiodiffusion Television Francaise (ORTF) and Nederlandse Omroep Stichting (NOS) techniques [4,7] place microphones slightly apart. In the ORTF technique, the microphone spacing is similar to the human ear spacing, while the spacing for the NOS technique is approximately 30 cm. In general, both coincident and near-coincident recording techniques utilize directional microphones to realize good directional characteristics [4]. However, with spaced recording techniques, including AB techniques [4,8], stereophonic images can be obtained by the ICTD between stereo microphones, because omni-directional microphones are often used in such techniques [4,9]. To date, numerous portable video and audio capture devices have been released to the market. These devices usually capture stereo audio as well as high-quality video. Unfortunately, because most portable devices are limited in size, and coincident or near-coincident recording techniques are most appropriate for such devices. However, when the audio signals captured by these recording techniques are reproduced, the stereophonic images often do not feel sufficient [10, 11, 12, 13]. This is because the body of a portable device equipped with directional microphones acts as wall reflection in a recording, which is referred to as shadowed directivity [10]. As an alternative, a spaced recording technique can be applied to capture stereo audio from such portable devices [11, 12, 13]. In this case, the width or length of the portable device body such as a smart phone or digital camera is approximately 10 cm, thus the allowable distance between two microphones is less than 3 cm. This hardware limitation makes it difficult to match the perceived azimuth angle of the reproduced sound source to the actual that of the original sound source, when a spaced recording technique is applied [8]. To mitigate this, a stereophonic image enhancement method using head-related transfer functions (HRTFs) was proposed in [11]. This method was more successful at enhancing stereophonic images than original stereo signals, but it had a somewhat limited sweet spot, and it was difficult to deliver reliable stereo quality to a listener located beyond this sweet spot. If the original stereo signals were nearly monaural signals, it is difficult to enhance a stereophonic image properly, even though the illusion of wider stereo loudspeaker spacing is created. [PERSON] _et al._ proposed a stereophonic image control method that linearly interpolated the spectra of the left and right channels in the frequency domain [12].