Compressive covariance sampling (CCS) theory aims to recover the covariance matrix (CM) of a signal, instead of the signal itself, from a reduced set of random linear projections. Although several theoretical works demonstrate the CCS theory’s advantages in compressive spectral imaging tasks, a real optical implementation has no been proposed. Therefore, this paper proposes a compressive spectral sensing protocol for the dual-dispersive coded aperture spectral snapshot imager (DD-CASSI) to directly estimate the covariance matrix of the signal. Specifically, we propose a coded aperture design that allows recasting the vector sensing problem into matrix form, which enables to exploit the covariance matrix structure such as positive-semidefiniteness, low-rank, or Toeplitz. Additionally, a low-rank approximation of the image is reconstructed using a Principal Components Analysis (PCA) based method. In order to test the precision of the reconstruction, some spectral signatures of the image are captured with a spectrometer and compared with those obtained in the reconstruction using the covariance matrix. Results show the reconstructed spectrum is accurate with a spectral angle mapper (SAM) of less than 14°. RGB image composites of the spectral image also provide evidence of a correct color reconstruction.

In most imaging applications the spatial resolution is a concern of the systems, but increasing the resolution of the sensor increases substantially the implementation cost. One option with lower cost is the use of spatial light modulators, which allows improving the reconstructed image resolution by including a high-resolution codification. In this paper, we propose a reconstruction methodology that exploits the intrinsic information contained in low-resolution measurements generated by the use of high-resolution spatial light modulators and high-resolution approximations obtained via a CNN. Specifically, based on a high-resolution CNN approximation, an l2fidelity regularization term is introduced into a traditional l2-l1optimization problem. Finally, the simulations of the proposed l2-l1-l2reconstruction approach show a quality improvement in up to 3.7dB in averaged PSNR against the use of the traditional l2-l1approach.

In recent years there has been an increasing interest in sensing devices that capture multidimensional information such as the spectral light field (SLF) images, which are 5-dimensional (5D) representations of a scene including 2D spatial, 2D angular and 1D spectral information. Spatio-spectral and angular information plays an important role in modern applications spanning from microscopy to computer vision. However, SLF sensors use expensive beam-splitters or cameras arrays placed in tandem, which split the sensing problem in two time consuming and independent tasks: spectral and light field imaging tasks. This work proposes a compressive spectral light field imaging architecture that builds on the principles of the compressive imaging framework, to capture multiplexed representations of the multidimensional information, so that, less measurements are required to capture the SLF data cube. Alongside, we propose a computational algorithm to recover the 5D information from the compressed measurements, exploiting the inherent high correlations within the SLF by treating them as 3D tensors. Furthermore, exploiting the geometry properties of the proposed optical architecture, the Tucker decomposition is applied to the set of compressed measurements, so that, an ad-hoc dictionary-like image representation basis is calculated online. This in turn, entails a more accurate reconstruction of the SLF since the dictionary fits the specific characteristics of the image itself. We demonstrate through simulations over three SLF datasets captured in our laboratory, and an experimental proof-of-concept implementation, that the proposed compressive imaging device together with the proposed computational algorithm represent an efficient alternative to capture SLF, compared to conventional methods that employ either side-information or multiple sensors. Also, we show that the tensor-based proposed algorithm exhibits a lower computational complexity than the matrix-based state of the art counterparts, thus enabling fast processing of multidimensional images.