A novel coded aperture for γ-ray imaging based on compressed sensing

High spatial resolution is of great significance for the γ -ray imaging technique, whose performance is mainly limited by the spatial resolution of position sensitive detectors (PSDs). In this work, the compressive coded aperture is introduced in γ -ray imaging as the basic pattern, and enlarged with the “mosaic” method to increase the Fully Coded Field of View (FCFV) of the PSDs. In order to demonstrate the performance of the compressive coded aperture, Monte-Carlo simulations of the encoding process have been performed for the mosaiced compressive coded aperture as well as the Modified Uniformly Redundant Arrays (MURA) coded aperture. The encoded image of the compressive coded aperture is reconstructed using the sparse reconstruction algorithm based on interior point method, with Discrete Cosine Transform (DCT) basis, Haar wavelet basis and Discrete Fourier Transform (DFT) basis respectively, and the encoded image of the MURA coded aperture is reconstructed respectively with the sparse method and the Maximum-Likelihood, Expectation-Maximization (MLEM) algorithm. In comparison with the MURA coded aperture reconstructed with the MLEM method, higher resolution images can be obtained from lower resolution detectors with both compressive coded aperture and MURA coded aperture using the sparse method. However, with the sparse method, the compressive coded aperture leads to higher quality images than the MURA coded aperture does.