Compressive imaging (CI) consists of reconstructing images from incomplete observed data. The reconstruction process involves solving an ill-posed inverse problem which is highly dependent on the number of real measurements, with a greater number of measurements typically leading to more accurate reconstructions. Due to their ability to learn data distributions, diffusion models (DM) have emerged as promising techniques for various inverse problems. Mainly, DMs solve inverse problems by conditioning the generation process to the acquired measurements. In this work, we introduce a new approach to improve this conditioning by exploiting synthetic measurements, which come from a synthetic sensing matrix. Synthetic measurements are estimated from real data via a neural network. The combined real and synthetic measurements form an augmented set, which is input into the conditional DM to enhance reconstruction capacity. Computational experiments demonstrate that augmenting measurements with the conditional DM improves performance compared to using only real measurements.

In remote sensing and environmental monitoring, the authenticity of the collected hyperspectral image (HSI) is critical since unauthorized changes could cause inaccurate evaluation. Traditional approaches ensure HSI integrity after the acquisition, leaving the data vulnerable to unauthorized access or modification before applying a protective strategy. In response, this work presents a pushbroom HSI system that integrates an authentication key on the acquisition process, ensuring the key imperceptibility without affecting performance in spectral classification tasks. In addition, this work develops an algorithm designed to simulate attacks through class modifications in the HSI. Additionally, a detection algorithm is proposed to identify modifications by comparing the signed HSI with the altered version, effectively recognizing the embedded key. The proposed method was tested using simulated data and acquired data in the optical laboratory. Results demonstrate that the system maintains classification accuracy, further enhancing imperceptibility. Additionally, modifications are detectable by the key with 99% accuracy.

In compressive imaging systems, the scene is acquired via linear coded noisy projections, known as measurements, requiring a recovery process to estimate the underlying signal. This recovery is inherently ill-posed, posing a challenge for accurate signal recovery. Existing methods that employ prior information about the signal often fail in practical scenarios. In this work, instead of developing a new prior over the signal, we exploit the structure of the low-dimensional measurements to synthesize an augmented measurement set that can be used in various recovery methods to improve its performance. We used a deep neural network to generate the synthetic measurements from the acquired data. We show the benefits of this approach in two schemes, deep learning-based recovery and the plug-and-play (PnP) algorithm. Particularly, our method is interpreted as a non-linear preconditioning technique for the PnP algorithm. We show improved performance for different sensing matrices.

In computational optical imaging and wireless communications, signals are acquired through linear coded and noisy projections, which are recovered through computational algorithms. Deep model-based approaches, i.e., neural networks incorporating the sensing operators, are the state-of-the-art for signal recovery. However, these methods require exact knowledge of the sensing operator, which is often unavailable in practice, leading to performance degradation. Consequently, we propose a new recovery paradigm based on knowledge distillation. A teacher model, trained with full or almost exact knowledge of a synthetic sensing operator, guides a student model with an inexact real sensing operator. The teacher is interpreted as a relaxation of the student since it solves a problem with fewer constraints, which can guide the student to achieve higher performance. We demonstrate the improvement of signal reconstruction in computational optical imaging for single-pixel imaging with miscalibrated coded apertures systems and multiple-input multiple-output symbols detection with inexact channel matrix.

Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior information is typically incorporated through handcrafted regularizers or learned models that constrain the solution space. However, these priors typically ignore the task-specific structure of that null-space. In this work, we propose Non-Linear Projections of the Null-Space (NPN), a novel class of regularization that, instead of enforcing structural constraints in the image domain, promotes solutions that lie in a low-dimensional projection of the sensing matrix's null-space with a neural network. Our approach has two key advantages: (1) Interpretability: by focusing on the structure of the null-space, we design sensing-matrix-specific priors that capture information orthogonal to the signal components that are fundamentally blind to the sensing process. (2) Flexibility: NPN is adaptable to various inverse problems, compatible with existing reconstruction frameworks, and complementary to conventional image-domain priors. We provide theoretical guarantees on convergence and reconstruction accuracy when used within plug-and-play methods. Empirical results across diverse sensing matrices demonstrate that NPN priors consistently enhance reconstruction fidelity in various imaging inverse problems, such as compressive sensing, deblurring, super-resolution, computed tomography, and magnetic resonance imaging, with plug-and-play methods, unrolling networks, deep image prior, and diffusion models.

Recent developments in spectrum-sharing technologies include integrated sensing and communications (ISAC) systems to save resources, cost, and power. In this paper, we consider a co-existence topology with n-tuple radar and communications transmitters, wherein neither the transmitted signal nor the channels are known. Estimating these unknown quantities is modeled as a n-tuple blind deconvolution problem (NTBD). The receiver is considered to be a uniform linear antenna array. Thus, the channels are modeled as continuous-valued time delay, Doppler modulation, and direction of arrival (DoA). Also, harnessing the sparse nature of the channels and their continuousvalued parametrization, we propose a 3D n-tuple atomic norm minimization (NANM). Casting the NANM problem to its corresponding dual optimization problem, and employing the theory of positive trigonometric polynomial, we formulate a semidefinite program for the estimation of the unknown channel parameters. Performance guarantees of the proposed algorithm are provided in terms of the minimum number of samples required for exact recovery. Finally, numerical simulations validate our theoretical insights.

Computational optical imaging (COI) systems have enabled the acquisition of high-dimensional signals through optical coding elements (OCEs). OCEs encode the high-dimensional signal in one or more snapshots, which are subsequently decoded using computational algorithms. Currently, COI systems are optimized through an end-to-end (E2E) approach, where the OCEs are modeled as a layer of a neural network and the remaining layers perform a specific imaging task. However, the performance of COI systems optimized through E2E is limited by the physical constraints imposed by these systems. This paper proposes a knowledge distillation (KD) framework for the design of highly physically constrained COI systems. This approach employs the KD methodology, which consists of a teacher-student relationship, where a high-performance, unconstrained COI system (the teacher), guides the optimization of a physically constrained system (the student) characterized by a limited number of snapshots. We validate the proposed approach, using a binary coded apertures single pixel camera for monochromatic and multispectral image reconstruction. Simulation results demonstrate the superiority of the KD scheme over traditional E2E optimization for the designing of highly physically constrained COI systems.

Signal processing over hypercomplex numbers arises in many optical imaging applications. In particular, spectral image or color stereo data are often processed using octonion algebra. Recently, the eight-band multispectral image phase recovery has gained salience, wherein it is desired to recover the eight bands from the phaseless measurements. In this letter, we tackle this hitherto unaddressed hypercomplex variant of the popular phase retrieval (PR) problem. We propose octonion Wirtinger flow (OWF) to recover an octonion signal from its intensity-only observation. However, contrary to the complex-valued Wirtinger flow, the non-associative nature of octonion algebra and the consequent lack of octonion derivatives make the extension to OWF non-trivial. We resolve this using the pseudo-real-matrix representation of octonion to perform the derivatives in each OWF update. We demonstrate that our approach recovers the octonion signal up to a right-octonion phase factor. Numerical experiments validate OWF-based PR with high accuracy under both noiseless and noisy measurements.

We consider a general spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown at the receiver. In this dual-blind deconvolution (DBD) problem, a common receiver admits the multi-carrier wireless communications signal that is overlaid with the radar signal reflected-off multiple targets. When the radar receiver is not collocated with the transmitter, such as in passive or multistatic radars, the transmitted signal is also unknown apart from the target parameters. Similarly, apart from the transmitted messages, the communications channel may also be unknown in dynamic environments such as vehicular networks. As a result, the estimation of unknown target and communications parameters in a DBD scenario is highly challenging. In this work, we exploit the sparsity of the channel to solve DBD by casting it as an atomic norm minimization problem. Our theoretical analyses and numerical experiments demonstrate perfect recovery of continuous-valued range-time and Doppler velocities of multiple targets as well as delay-Doppler communications channel parameters using uniformly-spaced time samples in the dual-blind receiver.

This paper presents an end-to-end (E2E) deep learning approach for the fusion of the data from two compressive spectral imaging systems, where a single neural network is developed to simultaneously optimize the sensing matrices and the decoder operator. The proposed E2E method models the sensing operator of the systems to fuse as optical layers, where the learnable parameters are the coded apertures of these CSI systems. These optical layers are then concatenated to an inspired unrolled deep neural network, where after training, these sensing matrices remain non-trainable along the optimization stages. Finally, a loss function is proposed. Simulation results show an improvement of the proposed coupled method compared with previous work and an enhancement due to the training of the sensing matrices and the proposed loss function.