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 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.