Compressive Covariance Matrix Estimation from a Dual-Dispersive Coded Aperture Spectral Imager

Abstract

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 o . RGB image composites of the spectral image also provide evidence of a correct color reconstruction.

JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging

“…We evaluated the proposed proposed method with real measurements provided by authors in [51] using a testbed implementation of a spatial-spectral DD-CASSI imaging system, shown in Fig. The compressed projection and spectral image have a spatial resolution of 256 × 256 pixels with characterization to recover up to 𝐶 = 31 spectral bands.…”

“…The compressed projection and spectral image have a spatial resolution of 256 × 256 pixels with characterization to recover up to 𝐶 = 31 spectral bands. The coded aperture designed in [51] is generated from a random binary pattern with 18% transmittance and acquires three snapshots. Based on the performance evaluation summarized in Table 2, DIP, ADMMnet, LDSR, and the proposed method are selected for the real data validation.…”