Orthogonal single-pixel imaging using an adaptive under-Nyquist sampling method

Single-pixel imaging (SPI) recently has made significant progress, however, it is still an open issue to adaptively tradeoff its imaging fidelity and speed. Here, we present an adaptive sampling method for SPI to reduce the sampling rate for improving the imaging speed adaptively, sacrificing as little as possible of its imaging fidelity. The proposed method only requires setting an error band to realize adaptive under-Nyquist sampling, based upon the fact that the coefficient matrix consisted of the frequency components obtained by the orthogonal transforms is sparse. First, an appropriately elaborated sampling path, which can be divided into multiple segments, can be set according to this coefficient matrix measured by a single-pixel detector. Then the variance of each segment is calculated and expressed in logarithmic form for the real-time polynomial curve fitting. When the variation of the curve’s slope is small enough and reaches an error band, the sampling is adaptively stopped. Finally, the object image can be reconstructed via the adaptive sampling method following the elaborated sampling path for improving the imaging speed adaptively. The effectiveness of the adaptive sampling SPIs based on the orthogonal transforms, such as Hadamard transform, discrete cosine transform, Fourier transform, and Krawtchouk moments transform, is theoretically and experimentally demonstrated. It should be noted the proposed method can be also applied in SPIs using other orthogonal transforms, in which only an error band is set by the users.