Untrained Neural Nets for Snapshot Compressive Imaging: Theory and Algorithms

Snapshot compressive imaging (SCI) recovers high-dimensional (3D) data cubes from a single 2D measurement, enabling diverse applications like video and hyperspectral imaging to go beyond standard techniques in terms of acquisition speed and efficiency. In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure. Such UNN-based methods are appealing as they have the potential of avoiding the computationally intensive retraining required for different source models and different measurement scenarios. We first develop a theoretical framework for characterizing the performance of such UNN-based methods. The theoretical framework, on the one hand, enables us to optimize the parameters of data-modulating masks, and on the other hand, provides a fundamental connection between the number of data frames that can be recovered from a single measurement to the parameters of the untrained NN. We also employ the recently proposed bagged-deep-image-prior (bagged-DIP) idea to develop SCI Bagged Deep Video Prior (SCI-BDVP) algorithms that address the common challenges faced by standard UNN solutions. Our experimental results show that in video SCI our proposed solution achieves state-of-the-art among UNN methods, and in the case of noisy measurements, it even outperforms supervised solutions.

Theoretical Analysis of Binary Masks in Snapshot Compressive Imaging Systems

Snapshot compressive imaging (SCI) systems have gained significant attention in recent years. While previous theoretical studies have primarily focused on the performance analysis of Gaussian masks, practical SCI systems often employ binary-valued masks. Furthermore, recent research has demonstrated that optimized binary masks can significantly enhance system performance. In this paper, we present a comprehensive theoretical characterization of binary masks and their impact on SCI system performance. Initially, we investigate the scenario where the masks are binary and independently identically distributed (iid), revealing a noteworthy finding that aligns with prior numerical results. Specifically, we show that the optimal probability of non-zero elements in the masks is smaller than 0.5. This result provides valuable insights into the design and optimization of binary masks for SCI systems, facilitating further advancements in the field. Additionally, we extend our analysis to characterize the performance of SCI systems where the mask entries are not independent but are generated based on a stationary first-order Markov process. Overall, our theoretical framework offers a comprehensive understanding of the performance implications associated with binary masks in SCI systems.

Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networks

Constraint solving is an elementary way for verification of deep neural networks (DNN). In the domain of AI safety, a DNN might be modified in its structure and parameters for its repair or attack. For such situations, we propose the incremental DNN verification problem, which asks whether a safety property still holds after the DNN is modified. To solve the problem, we present an incremental satisfiability modulo theory (SMT) algorithm based on the Reluplex framework. We simulate the most important features of the configurations that infers the verification result of the searching branches in the old solving procedure (with respect to the original network), and heuristically check whether the proofs are still valid for the modified DNN. We implement our algorithm as an incremental solver called DeepInc, and exerimental results show that DeepInc is more efficient in most cases. For the cases that the property holds both before and after modification, the acceleration can be faster by several orders of magnitude, showing that DeepInc is outstanding in incrementally searching for counterexamples. Moreover, based on the framework, we propose the multi-objective DNN repair problem and give an algorithm based on our incremental SMT solving algorithm. Our repair method preserves more potential safety properties on the repaired DNNs compared with state-of-the-art.