State-of-the-art snapshot spectral imaging (SI) systems introduce color-coded apertures (CCAs) into their setups to obtain a flexible spatial-spectral modulation, allowing spectral information to be reconstructed from a set of coded measurements. Besides the CCA, other optical elements, such as lenses, prisms, or beam splitters, are usually employed, making systems large and impractical. Recently, diffractive optical elements (DOEs) have partially replaced refractive lenses to drastically reduce the size of the SI devices. The sensing model of these systems is represented as a projection modeled by a spatially shift-invariant convolution between the unknown scene and a point spread function (PSF) at each spectral band. However, the height maps of the DOE are the only free parameters that offer changes in the spectral modulation, which causes the ill-posedness of the reconstruction to increase significantly. To overcome this challenge, our work explores the advantages of the spectral modulation of an optical setup composed of a DOE and a CCA. Specifically, the light is diffracted by the DOE and then filtered by the CCA, located close to the sensor. A shift-variant property of the proposed system is clearly evidenced, resulting in a different PSF for each pixel, where a symmetric structure constraint is imposed on the CCA to reduce the high number of resulting PSFs. Additionally, we jointly design the DOE and the CCA parameters with a fully differentiable image formation model using an end-to-end approach to minimize the deviation between the true and reconstructed image over a large set of images. Simulation shows that the proposed system improves the spectral reconstruction quality in up to 4 dB compared with current state-of-the-art systems. Finally, experimental results with a fabricated prototype in indoor and outdoor scenes validate the proposed system, where it can recover up to 49 high-fidelity spectral bands in the 420–660 nm.

Covering from photography to depth and spectral estimation, diverse computational imaging (CI) applications benefit from the versatile modulation of coded apertures (CAs). The lightwave fields as space, time, or spectral can be modulated to obtain projected encoded information at the sensor that is then decoded by efficient methods, such as the modern deep learning decoders. Although the CA can be fabricated to produce an analog modulation, a binary CA is preferred since more straightforward calibration, higher speed, and lower storage are achieved. As the performance of the decoder mainly depends on the structure of the CA, several works optimize the CA ensembles by customizing regularizers for a particular application without considering the critical physical constraints of the CAs. This work presents an end-to-end (E2E) deep learning-based optimization of CAs for CI tasks. The CA design method aims to cover a wide range of CI problems, easily changing the loss function of the deep approach. The designed loss function includes regularizers to fulfill the widely used sensing requirements of the CI applications. Mainly, the regularizers can be selected to optimize the transmittance, the compression ratio, and the correlation among measurements. At the same time, a binary CA solution is encouraged, and the performance of the CI task is maximized in applications such as restoration, classification, and semantic segmentation.

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow the identification of objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared with conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarizes the advances in CSI, starting with SI and its relevance and continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, as well as the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks.

Compressive spectral imaging (CSI) acquires compressed observations of a spectral scene by applying different coding patterns at each spatial location and then performing a spectral-wise integration. Relying on compressive sensing, spectral image reconstruction is achieved by using nonlinear and relatively expensive optimization-based algorithms. In the CSI literature, several works have focused on improving reconstructions quality by properly designing the set of coding patterns. However, signal recovery is not actually necessary in many signal processing applications. For instance, assuming that compressed measurements with similar characteristics lie on the same subspace, unsupervised methods such as subspace clustering can be used to separate them into the same cluster. Since the structure of compressed measurements is defined by the applied codification, it is possible to improve clustering performance. This paper proposes to design a set of coding patterns such that inter-class and intra-class data structure is preserved after the CSI acquisition in order to improve clustering results directly on the compressed domain. To validate the coding pattern design, an algorithm based on sparse subspace clustering (SSC) is proposed to perform clustering on the compressed measurements. The proposed algorithm adds a three-dimensional (3-D) spatial regularizer to the SSC problem exploiting the spatial correlation of spectral images. In general, an overall accuracy up to 83.81% is obtained, when noisy measurements are assumed. In addition, a difference of at most 4% in terms of overall accuracy was observed when comparing the clustering results obtained by the full 3-D data with those achieved using CSI measurements acquired with the proposed coding pattern design.

Recent advances in deep learning led to several algorithms for the accurate diagnosis of pneumonia from chest X-rays. However, these models require large training medical datasets, which are sparse, isolated, and generally private. Furthermore, these models in medical imaging are known to over-fit to a particular data domain source, i.e., these algorithms do not conserve the same accuracy when tested on a dataset from another medical center, mainly due to image distribution discrepancies. In this work, a domain adaptation and classification technique is proposed to overcome the over-fit challenges on a small dataset. This method uses a private-small dataset (target domain), a public-large labeled dataset from another medical center (source domain), and consists of three steps. First, it performs a data selection of the source domain’s most representative images based on similarity constraints through principal component analysis subspaces. Second, the selected samples from the source domain are fit to the target distribution through an image to image translation based on a cycle-generative adversarial network. Finally, the target train dataset and the adapted images from the source dataset are used within a convolutional neural network to explore different settings to adjust the layers and perform the classification of the target test dataset. It is shown that fine-tuning a few specific layers together with the selected-adapted images increases the sorting accuracy while reducing the trainable parameters. The proposed approach achieved a notable increase in the target dataset’s overall classification accuracy, reaching up to 97.78% compared to 90.03% by standard transfer learning.

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms.