In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.
We present a deep learning image reconstruction method called AirNet-SNL for sparse view computed tomography. It combines iterative reconstruction and convolutional neural networks with end-to-end training. Our model reduces streak artifacts from filtered back-projection with limited data, and it trains on randomly generated shapes. This work shows promise to generalize learning image reconstruction.
We present that distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l1-norm, l0-norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. In conclusion, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.
Distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l1-norm, l0-norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. As a result, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.
