There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate reductions in data-acquisition times. Deep learning-based methods hold potential for learning object priors or constraints that can serve to mitigate the effects of data-incompleteness on image reconstruction. One line of emerging research involves formulating an optimization-based reconstruction method in the latent space of a generative deep neural network. However, when generative adversarial networks (GANs) are employed, such methods can result in image reconstruction errors if the sought-after solution does not reside within the range of the GAN. To circumvent this problem, in this work, a framework for reconstructing images from incomplete measurements is proposed that is formulated in the latent space of invertible neural network-based generative models. A novel regularization strategy is introduced that takes advantage of the multiscale architecture of certain invertible neural networks, which can result in improved reconstruction performance over classical methods in terms of traditional metrics. The proposed method is investigated for reconstructing images from undersampled MRI data. The method is shown to achieve comparable performance to a state-of-the-art generative model-based reconstruction method while benefiting from a deterministic reconstruction procedure and easier control over regularization parameters.

Single-image super-resolution (SISR) is a classic image restoration operation that seeks to estimate a high-resolution (HR) image from an observed low-resolution (LR) one.¹ A variety of methods have been developed to achieve this goal, such as filtering and interpolation-based approaches² and more formal regularized inverse problem-based formulations,^3,4 to name a few. Recently, deep learning-based image super-resolution (DL-SR) methods have been widely employed and have shown great promise for SISR in terms of traditional image quality (IQ) metrics such as mean square error (MSE), structural similarity index metric (SSIM), and peak-signal-to-noise ratio (PSNR).^{5 – 8}

Multiphoton microscopy (MPM) refers to an ensemble of imaging modalities that involve the simultaneous interaction of multiple photons with a material. MPM often requires longer illumination wavelengths (above 700 nm) compared to standard confocal microscopy, reducing optical absorption and scattering in biological tissues, thereby limiting tissue damage¹ and increasing the penetration depth.² Owing to its reduced photobleaching beyond the imaging planes,³ two- and three-photon fluorescence MPM modalities have been used for in vivo imaging of zebrafish pregnancy⁴ and observation of serotonin distribution in living cells,⁵ respectively. MPM techniques involving nonlinear scattering such as second-^6,7 and third-harmonic generation^8,9 (SHG and THG, respectively) take advantage of endogenous second- and third-order nonlinearities in biological systems leading to label-free imaging and tissue specificity. For example, SHG and THG microscopy have been used to differentiate healthy and injured horse tendon¹⁰ and study lymphocyte distribution in breast tissue biopsies, respectively.⁹

Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been actively investigated for regularizing image reconstruction problems by learning a prior for the object properties from training images. However, an analysis of the prior information learned by these deep networks and their ability to generalize to data that may lie outside the training distribution is still being explored. An inaccurate prior might lead to false structures being hallucinated in the reconstructed image and that is a cause for serious concern in medical imaging. In this work, we propose to illustrate the effect of the prior imposed by a reconstruction method by decomposing the image estimate into generalized measurement and null components. The concept of a hallucination map is introduced for the general purpose of understanding the effect of the prior in regularized reconstruction methods. Numerical studies are conducted corresponding to a stylized tomographic imaging modality. The behavior of different reconstruction methods under the proposed formalism is discussed with the help of the numerical studies.

Obtaining a useful estimate of an object from highly incomplete imaging measurements remains a holy grail of imaging science. Deep learning methods have shown promise in learning object priors or constraints to improve the conditioning of an ill-posed imaging inverse problem. In this study, a framework for estimating an object of interest that is semantically related to a known prior image, is proposed. An optimization problem is formulated in the disentangled latent space of a style-based generative model, and semantically meaningful constraints are imposed using the disentangled latent representation of the prior image. Stable recovery from incomplete measurements with the help of a prior image is theoretically analyzed. Numerical experiments demonstrating the superior performance of our approach as compared to related methods are presented.