Advanced imaging via multiplexed sensing and compressive sensing

This dissertation works on advanced imaging systems using multiplexed sensing and compressive sensing (CS). Conventional cameras (e.g., pin-hole and lens cameras) follow the one-object-point-to-one-image-point or one-to-one (OTO) mapping model. Multipled sensing and compressive sensing attempt to improve conventional OTO cameras by exploring other object-to-image mapping models, such as one-to-multiple (OTM) divergent mapping, multipleto- one (MTO) convergent mapping and multiple-to-multiple (MTM) random mapping, and respectively achieve two different advanced imaging functions. On one hand, multiplexed sensing attempts to acquire multi-modality information from the outside scene by multi-channel sensing and fuses a more informative image. On the other hand, compressive sensing, also called compressive sampling, aims at acquiring a signal/image at a lower sampling rate (below the Nyquist rate) by exploiting (1) the MTM random sampling and (2) the prior knowledge that a signal/image is sparse or correlated in some domain.;The first design is a multiplexed imaging system that accesses and manipulates the lens aperture for many computational imaging applications. Multiplexed imaging often involves manipulating the incoming light beam on the aperture, which is located inside the lens housing and thus is challenging to access or modulate. In this system, a novel approach is proposed to provide an external aperture that enables dynamic control of its transmission, position and orientation. Specifically, a rear-attached relay system (lens) is mounted behind the imaging lens to reposition the aperture plane outside the imaging lens. The physical implementation of the multiplexed imaging system is presented to show (1) the effectiveness of providing access to the aperture and (2) the advantages of aperture manipulation in computational imaging applications.;The second design is a hybrid compressive sensing camera for image acquisition. First, this hybrid compressive sensing camera further reduces the sampling rate of compressive sensing by combining the traditional MTM random sampling with MTO low-resolution sampling. In addition, we propose a new L1-norm based total-variation measure TVL1, which enforces the sparsity and the directional continuity in the partial gradient domain. Theoretical and experimental results show that this new TVL1 achieves higher recovery accuracy than the previous TV measure TVL1L2 in decoding images from compressive measurements.;The third design is a three-dimensional compressive sensing (3DCS) camera for video acquisition. Despite the remarkable progress in the compressive sensing theory, little headway has been made in the compressive imaging (CI) camera and the required sampling rate for acquiring an image or video is still high. We propose a three-dimensional compressive sensing (3DCS) approach, which decodes a video from incomplete random samples by exploiting its 3D piecewise smoothness and temporal low-rank property. Experimental results show that 3DCS can reduce the required sampling rate for video acquisition to a practical level (i.e., 10%). In addition, an efficient decoding algorithm is developed for this 3DCS with guaranteed convergence. Finally, a promising physical implementation of the 3DCS camera using circulant sampling (or random convolution) is presented and a new random lens is presented to simplify the traditional random convolution implementation, i.e., four-dimensional correlator in Fourier optics. This random lens has much higher light-gathering power and higher imaging quality than other simple implementations, such as coded aperture, random pinhole array and random mirror array.;In addition to sparsity and total variation, low-rankness is another new and encouraging measure in compressive sensing. However, robust low-rank recovery from compressive measurements is a time-consuming process and even its state-of-the-art (robust principal component analysis or RPCA) has a cubic complexity. The fourth design is an efficient low-rank recovery approach, called robust orthonormal subspace learning (ROSL). Compared with RPCA using nuclear norm, ROSL presents a novel rank measure that imposes the group sparsity under orthonormal subspace, which enables it to recover a low-rank matrix by fast sparse coding. Theoretical bounds are given to prove that minimizing this rank measure has the same global minimum as the nuclear norm minimization. In addition, an efficient algorithm (alternating direction method and block coordinate descent) is developed for ROSL and a random sampling algorithm is introduced to further accelerate ROSL such that ROSL+ has linear complexity of the matrix size. Extensive evaluations demonstrate that ROSL and ROSL+ achieve the state-of-art efficiency in low-rank recovery without compromising the accuracy.;The fifth design is a non-local compressive sensing (NLCS) camera for image acquisition. While 3DCS achieves a low required sampling rate for video acquisition, image CS still requires a high sampling rate. Motivated by the non-local mean approaches in image restoration, a non-local compressive sensing (NLCS) recovery method is proposed, which further reduces the sampling rate by exploiting the non-local patch correlation and the local piecewise smoothness in natural images. Two non-local sparsity measures, i.e., non-local wavelet sparsity and non-local joint sparsity, are proposed to obtain patch correlation in NLCS. In addition, an efficient iterative algorithm is developed to solve the NLCS recovery problem, which is shown to have stable convergence behavior in experiments. The experimental results show that our NLCS significantly improves the state-of-the-art image CS and that non-local joint sparsity is better than non-local wavelet sparsity in terms of recovery accuracy.