Single-Pixel imaging for capturing the shape of three-dimensional objects

Abstract

In [1], single-pixel imaging was proposed in order to reduce size and complexity of optical components. Single-pixel imaging is based on projecting a series of random patterns and measuring the reflected sum intensity. The recovery from the measured intensities can be written as a compressed sensing problem. For sparse images or images that have a sparse representation, accurate reconstruction is possible, even if the number of measurements is much lower than the number of pixels to be recovered. In [2], Bayesian Approximate Message Passing (BAMP) was proposed as a low-complexity iterative algorithm for recovering sparse vectors from few measurements. For the application of the BAMP algorithm, the measurement matrix has to be reformulated to fulfill certain properties. Three-dimensional (3D) single-pixel imaging suffers from high complexity and large storage requirements, which arise already at the sensing stage. The volume of interest is divided into volume elements (voxels) and an intensity value is assigned to each voxel. If the volume is divided into 100 voxels in each direction (a total of 10 6 voxels) and is sampled at a rate of 0.5, the sampling matrix would have 0.5·10 6 ·10 6 = 5·10 11 entries. In this work, the reduction of the memory required for storing the measurement matrix is investigated. In particular, 3 different techniques for sampling 3D images are considered and for each of these techniques a BAMP based approach with lower memory requirement is proposed. The simulations conducted show that the presented approaches reduce the memory requirement while still achieving good results.

In [1], single-pixel imaging was proposed in order to reduce size and complexity of optical components. Single-pixel imaging is based on projecting a series of random patterns and measuring the reflected sum intensity. The recovery from the measured intensities can be written as a compressed sensing problem. For sparse images or images that have a sparse representation, accurate reconstruction is possible, even if the number of measurements is much lower than the number of pixels to be recovered. In [2], Bayesian Approximate Message Passing (BAMP) was proposed as a low-complexity iterative algorithm for recovering sparse vectors from few measurements. For the application of the BAMP algorithm, the measurement matrix has to be reformulated to fulfill certain properties. Three-dimensional (3D) single-pixel imaging suffers from high complexity and large storage requirements, which arise already at the sensing stage. The volume of interest is divided into volume elements (voxels) and an intensity value is assigned to each voxel. If the volume is divided into 100 voxels in each direction (a total of 10 6 voxels) and is sampled at a rate of 0.5, the sampling matrix would have 0.5·10 6 ·10 6 = 5·10 11 entries. In this work, the reduction of the memory required for storing the measurement matrix is investigated. In particular, 3 different techniques for sampling 3D images are considered and for each of these techniques a BAMP based approach with lower memory requirement is proposed. The simulations conducted show that the presented approaches reduce the memory requirement while still achieving good results.