A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging

Abstract

Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging modalities such as hyper-spectral imaging, depth mapping, 3D profiling. However, the single-pixel technique requires sequential measurements resulting in a trade-off between spatial resolution and acquisition time, limiting real-time video applications to relatively low resolutions. Compressed sensing techniques can be used to improve this trade-off. However, in this low resolution regime, conventional compressed sensing techniques have limited impact due to lack of sparsity in the datasets. Here we present an alternative compressed sensing method in which we optimize the measurement order of the Hadamard basis, such that at discretized increments we obtain complete sampling for different spatial resolutions. In addition, this method uses deterministic acquisition, rather than the randomized sampling used in conventional compressed sensing. This so-called ‘Russian Dolls’ ordering also benefits from minimal computational overhead for image reconstruction. We find that this compressive approach performs as well as other compressive sensing techniques with greatly simplified post processing, resulting in significantly faster image reconstruction. Therefore, the proposed method may be useful for single-pixel imaging in the low resolution, high-frame rate regime, or video-rate acquisition.

Single-pixel 3D reconstruction via a high-speed LED array

“…The improvements are achieved by choosing a chromatic LED chip with a small size (SMD18-038BT, chip size 1.3 mm). Hadamard matrix is used for the mask patterns, which had a small computational overhead [26]. To display Hadamard patterns efficiently, the same two consecutive display strategy from [28] is employed here, with 128 I/O ports.…”

“…In single-pixel imaging, the number of mask patterns required for one image reconstruction is proportional to the pixel resolution of the image, therefore limiting the frame rate of the system. One approach is to decrease the required number via compressive sensing algorithms of different sophistications [20][21][22][23][24][25][26]. However, these algorithms either have a computational overhead or are incapable of reaching a significant low compressive ratio.…”

Time-domain terahertz compressive imaging

“…One of the most commonly used is the one derived from the Hadamard matrix, which has been proved to be good in signal-to-noise ratio (SNR) maximization [27]. In this work, we made use of an optimized ordering of the Hadamard set, as proposed by M.J. Sun et al [31], in which the spatial frequencies content of each pattern increases progressively. By using this scheme, most of the information related to the image will be contained in the first patterns.…”

“…By using this scheme, most of the information related to the image will be contained in the first patterns. This allows to decrease the acquisition time (by reducing the number of measurements required to reconstruct the image), while avoiding the calculation burden usually necessary for compressive sensing schemes based on random pattern sets [31]. For the image reconstruction, we made use of a non-iterative single-pixel algorithm, as reported by L. Bian et al [32].…”

Multi-resolution progressive computational ghost imaging

“…If the target area can be locked by a low-resolution image with a small number of measurements, then we only need to modulate the light fields corresponding to the target area, and the imaging speed can be obviously improved when an optimized coded illumination source is used. So in this paper, we propose a multi-resolution progressive computational ghost imaging (MPGI) method which is rooted in the application of Hadamard transform [15] and the ideas of progressive transmission [16].The reordered Hadamard derived pattern is utilized in processings of low resolution location and multi-resolution imaging. Since Hadamard matrix is orthogonal and symmetric, the effect of the correlated noise can be eliminated, and the image of the target can be reconstructed accurately.…”