Because of the physical constraints of light traveling in straight lines, the field of view of a detector is limited by non-transparent obstacles and conventional imaging systems cannot detect target scenes outside the field of view. Regions outside the line of sight, such as those hidden around corners, are generally referred to as non-line-of-sight (NLOS) areas. NLOS imaging has garnered the attention of researchers in various fields, including machine vision, remote sensing, medical imaging, and autonomous driving. NLOS imaging based on a single-photon detector array offers the advantages of high detection efficiency and speed. However, NLOS imaging based on a single-photon detector array results in a non-confocal form and an efficient and high-quality image-recovery algorithm is not yet available, which limits its further development. This study aims to improve the image-recovery quality of hidden objects under the conditions of non-confocal measurements provided by a single-photon detector array.

A technical approach for image recovery in NLOS imaging based on a single-photon detector array is presented, which involves converting the measurements under a single-photon detector array to confocal ones and then applying an image-restoration algorithm based on a convolutional approximation. The main concept of confocal measurement emulation involves selecting a new confocal point (the new illumination point overlaps with the new imaging point) outside the initial illumination and imaging points within the non-confocal detection model. For the non-confocal measurement in each time bin, an optimal spherical radius is selected such that a sphere centered at the new confocal point achieves the best fit with the ellipsoidal model for the initial non-confocal measurement. The confocalization process primarily comprises two aspects: rapid localization and ellipsoidal interpolation. Utilizing the recorded temporal range of several detection points, the envelope of the hidden object can be localized by ellipsoidal backprojection at high speed, which provides a specific area for the subsequent processing. Ellipsoidal interpolation exploits the advantage wherein the ellipsoidal section within a predetermined area can be refined to obtain more accurate timing information with respect to the new confocal point. Consequently, the emulated confocal measurements show better timing accuracy than the initial recording information determined by the detector. Subsequently, a convolutional approximation algorithm for image recovery is employed, which builds the convolutional relationship hidden inside the scene parameters between the backprojection result and the actual albedo. By implementing the deconvolution based on fast Fourier transforms, a closed-form solution for the recovered image can be obtained rapidly and accurately. Upon investigating the convolutional relationship, this approach not only reduces computational complexity but also allows for the incorporation of prior information, thus further enhancing the image quality. By combining the enhanced timing accuracy provided by the confocalization method with the high resolution provided by the convolutional approximation, high-quality recovery images of hidden objects can be achieved.

In the simulation, two “E”-shaped objects with different sizes made of white cardboard were used as the NLOS hidden objects to evaluate the resolution achieved by the proposed approach and to compare the results obtained using different image-recovery algorithms. The illumination point was set at the center of the right edge of the field of view to avoid the pile-up effect of the single-photon detectors in the array. The root mean square errors (RMSEs) of the reconstructed images obtained using the proposed convolutional approximation algorithm combined with the confocalization of non-confocal measurements for objects of each size were lower than those obtained using filtered-backprojection-based (FBP-based) or light-cone-transform-based (LCT-based) algorithms. The advantages of the proposed approach are more pronounced for smaller hidden objects or a smaller field of view for detection. Furthermore, an experimental setup for NLOS imaging was designed and constructed. Initially, non-confocal measurements were performed using a pulsed laser and a single photon avalanche diode (SPAD) array. The original time resolution of the SPAD in the experiments is approximately 57 ps. With the measurements transformed into emulated confocal ones, a timing accuracy of approximately 30 ps is achieved, thus validating the improvement in time resolution beyond that of the original detector achieved via the confocalization process. Subsequently, the image of the hidden object was reconstructed using the FBP-based, LCT-based, and proposed algorithms on the confocalized data. For “E”- and “H”-shaped objects, the proposed convolutional-approximation algorithm achieved RMSEs of 0.3314 and 0.2730 with respect to the ground truth, respectively; the FBP-based algorithm achieved 0.3770 and 0.3060, respectively; and the LCT-based algorithm achieved 0.3566 and 0.2986, respectively. Hence, the image-restoration performance of the proposed algorithms is superior to those of existing ones.

In summary, the confocalization of non-confocal measurements combined with a convolutional approximation algorithm can provide a new feasible route for NLOS imaging based on a single-photon detector array. Simulation and experimental results show that the technique proposed herein offers more advantages than conventional algorithms based on FPB or LCT, with lower recovery errors. This study is significant for the advancement of NLOS imaging.