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Compared to classical optical coherence theory based on Maxwell's electromagnetic theory and Glauber's quantum optical coherence theory based on matrix mechanics formulation of quantum mechanics, quantum optical coherence theory based on Feynman's path integral formulation of quantum mechanics provides a novel tool to study optical coherence. It has the advantage of understanding the connection between mathematical calculations and physical interpretations better. Quantum optical coherence theory based on Feynman's path integral is introduced and reviewed in this paper. Based on the results of transient first-order interference of two independent light beams, it is predicted that the classical model for electric field of thermal light introduced by classical optical textbooks may not be accurate. The physics of two-photon bunching of thermal light and Hong-Ou-Mandel dip of entangled photon pairs is the same, which can be interpreted by constructive and destructive two-photon interference, respectively. Quantum optical coherence theory based on Feynman's path integral is helpful to understand the coherence properties of light, which may eventually lead us to the answer of the question: what is a photon?, Comment: 40 pages, 35 figures

An elusive goal in navigation research is to build an intelligent agent that can understand multimodal instructions including natural language and image, and perform useful navigation. To achieve this, we study a widely useful category of navigation tasks we call Multimodal Instruction Navigation with demonstration Tours (MINT), in which the environment prior is provided through a previously recorded demonstration video. Recent advances in Vision Language Models (VLMs) have shown a promising path in achieving this goal as it demonstrates capabilities in perceiving and reasoning about multimodal inputs. However, VLMs are typically trained to predict textual output and it is an open research question about how to best utilize them in navigation. To solve MINT, we present Mobility VLA, a hierarchical Vision-Language-Action (VLA) navigation policy that combines the environment understanding and common sense reasoning power of long-context VLMs and a robust low-level navigation policy based on topological graphs. The high-level policy consists of a long-context VLM that takes the demonstration tour video and the multimodal user instruction as input to find the goal frame in the tour video. Next, a low-level policy uses the goal frame and an offline constructed topological graph to generate robot actions at every timestep. We evaluated Mobility VLA in a 836m^2 real world environment and show that Mobility VLA has a high end-to-end success rates on previously unsolved multimodal instructions such as "Where should I return this?" while holding a plastic bin. A video demonstrating Mobility VLA can be found here: https://youtu.be/-Tof__Q8_5s

The explosion of massive urban data recently has provided us with a valuable opportunity to gain deeper insights into urban regions and the daily lives of residents. Urban region representation learning emerges as a crucial realm for fulfilling this task. Among deep learning approaches, graph neural networks (GNNs) have shown promise, given that city elements can be naturally represented as nodes with various connections between them as edges. However, many existing GNN approaches encounter challenges such as over-smoothing and limitations in capturing information from nodes in other regions, resulting in the loss of crucial urban information and a decline in region representation performance. To address these challenges, we leverage urban graph structure information and introduce a hierarchical graph pooling process called Coarsened Graph Attention Pooling (CGAP). CGAP features local attention units to create coarsened intermediate graphs and global features. Additionally, by incorporating urban region graphs and global features into a global attention layer, we harness relational information to enhance representation effectiveness. Furthermore, CGAP integrates region attributes such as Points of Interest (POIs) and inter-regional contexts like human mobility, enabling the exploitation of multi-modal urban data for more comprehensive representation learning. Experiments on three downstream tasks related to the UN Sustainable Development Goals validate the effectiveness of region representations learned by our approach. Experimental results and analyses demonstrate that CGAP excels in various socioeconomic prediction tasks compared to competitive baselines.

This paper studies an infinite time horizon LQR optimal control problem for a system describing, within a linear approximation, the vertical oscillations of a floating solid, coupled to the motion of the free boundary fluid on which it floats. The fluid flow is described by a viscous version of the linearized Saint-Venant equations (shallow water regime). The major difficulty we are facing is that the domain occupied by the fluid is unbounded so that the system is not exponentially stable. This fact firstly raises challenges in proving the wellposedness, requiring the combined use of analytic semigroup theory and of an interpolation technique. The main contribution of the paper is that we show that, in spite of the lack of exponential stabilizability, we can define a wellposed LQR problem for which a Riccati based approach to design feedback controls can be implemented., Comment: 22 pages and 1 figure

Remote heart rate measurement is an increasingly concerned research field, usually using remote photoplethysmography (rPPG) to collect heart rate information through video data collection. However, in certain specific scenarios (such as low light conditions, intense lighting, and non-line-of-sight situations), traditional imaging methods fail to capture image information effectively, that may lead to difficulty or inability in measuring heart rate. To address these limitations, this study proposes using ghost imaging as a substitute for traditional imaging in the aforementioned scenarios. The mean absolute error between experimental measurements and reference true values is 4.24 bpm.Additionally, the bucket signals obtained by the ghost imaging system can be directly processed using digital signal processing techniques, thereby enhancing personal privacy protection., Comment: 4 pages, 6 figures

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.

In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters, resulting in a family of separated subgraphs. We individually employ the local graph convolution units as the local structure to further compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. Since these subgraphs are separated by different clusters and the structural information cannot be propagated between them, the local convolution operation can significantly avoid the over-smoothing problem caused by message passing through edges in most existing Graph Neural Networks (GNNs). By hierarchically performing the proposed procedures on the resulting coarsened graph, the proposed SSHPool can effectively extract the hierarchical global features of the original graph structure, encapsulating rich intrinsic structural characteristics. Furthermore, we develop an end-to-end GNN framework associated with the SSHPool module for graph classification. Experimental results demonstrate the superior performance of the proposed model on real-world datasets.

Data-driven methods have great advantages in modeling complicated human behavioral dynamics and dealing with many human-robot interaction applications. However, collecting massive and annotated real-world human datasets has been a laborious task, especially for highly interactive scenarios. On the other hand, algorithmic data generation methods are usually limited by their model capacities, making them unable to offer realistic and diverse data needed by various application users. In this work, we study trajectory-level data generation for multi-human or human-robot interaction scenarios and propose a learning-based automatic trajectory generation model, which we call Multi-Agent TRajectory generation with dIverse conteXts (MATRIX). MATRIX is capable of generating interactive human behaviors in realistic diverse contexts. We achieve this goal by modeling the explicit and interpretable objectives so that MATRIX can generate human motions based on diverse destinations and heterogeneous behaviors. We carried out extensive comparison and ablation studies to illustrate the effectiveness of our approach across various metrics. We also presented experiments that demonstrate the capability of MATRIX to serve as data augmentation for imitation-based motion planning., Comment: IEEE International Conference on Robotics and Automation (ICRA 2024)

Vision language models (VLMs) have shown impressive capabilities across a variety of tasks, from logical reasoning to visual understanding. This opens the door to richer interaction with the world, for example robotic control. However, VLMs produce only textual outputs, while robotic control and other spatial tasks require outputting continuous coordinates, actions, or trajectories. How can we enable VLMs to handle such settings without fine-tuning on task-specific data? In this paper, we propose a novel visual prompting approach for VLMs that we call Prompting with Iterative Visual Optimization (PIVOT), which casts tasks as iterative visual question answering. In each iteration, the image is annotated with a visual representation of proposals that the VLM can refer to (e.g., candidate robot actions, localizations, or trajectories). The VLM then selects the best ones for the task. These proposals are iteratively refined, allowing the VLM to eventually zero in on the best available answer. We investigate PIVOT on real-world robotic navigation, real-world manipulation from images, instruction following in simulation, and additional spatial inference tasks such as localization. We find, perhaps surprisingly, that our approach enables zero-shot control of robotic systems without any robot training data, navigation in a variety of environments, and other capabilities. Although current performance is far from perfect, our work highlights potentials and limitations of this new regime and shows a promising approach for Internet-Scale VLMs in robotic and spatial reasoning domains. Website: pivot-prompt.github.io and HuggingFace: https://huggingface.co/spaces/pivot-prompt/pivot-prompt-demo.

People employ expressive behaviors to effectively communicate and coordinate their actions with others, such as nodding to acknowledge a person glancing at them or saying "excuse me" to pass people in a busy corridor. We would like robots to also demonstrate expressive behaviors in human-robot interaction. Prior work proposes rule-based methods that struggle to scale to new communication modalities or social situations, while data-driven methods require specialized datasets for each social situation the robot is used in. We propose to leverage the rich social context available from large language models (LLMs) and their ability to generate motion based on instructions or user preferences, to generate expressive robot motion that is adaptable and composable, building upon each other. Our approach utilizes few-shot chain-of-thought prompting to translate human language instructions into parametrized control code using the robot's available and learned skills. Through user studies and simulation experiments, we demonstrate that our approach produces behaviors that users found to be competent and easy to understand. Supplementary material can be found at https://generative-expressive-motion.github.io/.

Foundation models that incorporate language, vision, and more recently actions have revolutionized the ability to harness internet scale data to reason about useful tasks. However, one of the key challenges of training embodied foundation models is the lack of data grounded in the physical world. In this paper, we propose AutoRT, a system that leverages existing foundation models to scale up the deployment of operational robots in completely unseen scenarios with minimal human supervision. AutoRT leverages vision-language models (VLMs) for scene understanding and grounding, and further uses large language models (LLMs) for proposing diverse and novel instructions to be performed by a fleet of robots. Guiding data collection by tapping into the knowledge of foundation models enables AutoRT to effectively reason about autonomy tradeoffs and safety while significantly scaling up data collection for robot learning. We demonstrate AutoRT proposing instructions to over 20 robots across multiple buildings and collecting 77k real robot episodes via both teleoperation and autonomous robot policies. We experimentally show that such "in-the-wild" data collected by AutoRT is significantly more diverse, and that AutoRT's use of LLMs allows for instruction following data collection robots that can align to human preferences., Comment: 26 pages, 9 figures, ICRA 2024 VLMNM Workshop

Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size differences. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in the training recipe, including data quality, training pipeline, and VLM architecture. Our work features the first internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Project website: https://spatial-vlm.github.io/

The essential of navigation, perception, and decision-making which are basic tasks for intelligent robots, is to estimate necessary system states. Among them, navigation is fundamental for other upper applications, providing precise position and orientation, by integrating measurements from multiple sensors. With observations of each sensor appropriately modelled, multi-sensor fusion tasks for navigation are reduced to the state estimation problem which can be solved by two approaches: optimization and filtering. Recent research has shown that optimization-based frameworks outperform filtering-based ones in terms of accuracy. However, both methods are based on maximum likelihood estimation (MLE) and should be theoretically equivalent with the same linearization points, observation model, measurements, and Gaussian noise assumption. In this paper, we deeply dig into the theories and existing strategies utilized in both optimization-based and filtering-based approaches. It is demonstrated that the two methods are equal theoretically, but this equivalence corrupts due to different strategies applied in real-time operation. By adjusting existing strategies of the filtering-based approaches, the Monte-Carlo simulation and vehicular ablation experiments based on visual odometry (VO) indicate that the strategy adjusted filtering strictly equals to optimization. Therefore, future research on sensor-fusion problems should concentrate on their own algorithms and strategies rather than state estimation approaches.

Generalization remains one of the most important desiderata for robust robot learning systems. While recently proposed approaches show promise in generalization to novel objects, semantic concepts, or visual distribution shifts, generalization to new tasks remains challenging. For example, a language-conditioned policy trained on pick-and-place tasks will not be able to generalize to a folding task, even if the arm trajectory of folding is similar to pick-and-place. Our key insight is that this kind of generalization becomes feasible if we represent the task through rough trajectory sketches. We propose a policy conditioning method using such rough trajectory sketches, which we call RT-Trajectory, that is practical, easy to specify, and allows the policy to effectively perform new tasks that would otherwise be challenging to perform. We find that trajectory sketches strike a balance between being detailed enough to express low-level motion-centric guidance while being coarse enough to allow the learned policy to interpret the trajectory sketch in the context of situational visual observations. In addition, we show how trajectory sketches can provide a useful interface to communicate with robotic policies: they can be specified through simple human inputs like drawings or videos, or through automated methods such as modern image-generating or waypoint-generating methods. We evaluate RT-Trajectory at scale on a variety of real-world robotic tasks, and find that RT-Trajectory is able to perform a wider range of tasks compared to language-conditioned and goal-conditioned policies, when provided the same training data., Comment: Evaluation videos can be found at https://rt-trajectory.github.io/

Large, high-capacity models trained on diverse datasets have shown remarkable successes on efficiently tackling downstream applications. In domains from NLP to Computer Vision, this has led to a consolidation of pretrained models, with general pretrained backbones serving as a starting point for many applications. Can such a consolidation happen in robotics? Conventionally, robotic learning methods train a separate model for every application, every robot, and even every environment. Can we instead train generalist X-robot policy that can be adapted efficiently to new robots, tasks, and environments? In this paper, we provide datasets in standardized data formats and models to make it possible to explore this possibility in the context of robotic manipulation, alongside experimental results that provide an example of effective X-robot policies. We assemble a dataset from 22 different robots collected through a collaboration between 21 institutions, demonstrating 527 skills (160266 tasks). We show that a high-capacity model trained on this data, which we call RT-X, exhibits positive transfer and improves the capabilities of multiple robots by leveraging experience from other platforms. More details can be found on the project website https://robotics-transformer-x.github.io., Comment: Project website: https://robotics-transformer-x.github.io

Interactive behavior modeling of multiple agents is an essential challenge in simulation, especially in scenarios when agents need to avoid collisions and cooperate at the same time. Humans can interact with others without explicit communication and navigate in scenarios when cooperation is required. In this work, we aim to model human interactions in this realistic setting, where each agent acts based on its observation and does not communicate with others. We propose a framework based on distributed potential games, where each agent imagines a cooperative game with other agents and solves the game using its estimation of their behavior. We utilize iLQR to solve the games and closed-loop simulate the interactions. We demonstrate the benefits of utilizing distributed imagined games in our framework through various simulation experiments. We show the high success rate, the increased navigation efficiency, and the ability to generate rich and realistic interactions with interpretable parameters. Illustrative examples are available at https://sites.google.com/berkeley.edu/distributed-interaction., Comment: 8 pages, 7 figures

Optical phased arrays (OPA) with high integration, fast speed, low power consumption, and high steering resolution are critical components in the emerging photonic integrated circuit (PIC), LiDAR, free space optical communication, 3D printing, and so on. According to the OPA working principle, its function is generally achieved by independently controlling the phase of the array elements. In practice, this presents a major challenge to overcome critical trade-offs of the element numbers, the control electronics, and the power consumption. Here, we give an alternative OPA solution to overcome this technical limitation, in the form of a cascaded periodically poled electro-optical crystal structure. Compared with the existing OPA scheme, only one control electronics is used to control the entire array elements in the current proposal, regardless of the number of array elements, implying higher integration and lower power consumption. With the help of the fast response properties of electro-optic crystal materials, a high-speed and high-resolution beam steering device is demonstrated. Simulating results show that the angular resolution can be improved by several orders of magnitude when the number of the cascaded-layer increases. An OPA prototype of a 6-layer cascaded periodically poled LiNbO$_3$ (cascaded-PPLN) was designed, fabricated, and characterized. The experiment that observed beam deflection in cascaded-PPLN OPA agrees well with the simulation results. Meantime, by demonstrating dynamic beam steering continually, its capability of continuous scanning and continually active phase tunability has been verified. Therefore, this cascaded periodically poled electro-optical crystal OPA offers a feasible direction of miniaturization and low power consumption for the optical system, such as the PIC system.

Slip is a very common phenomena present in wheeled mobile robotic systems. It has undesirable consequences such as wasting energy and impeding system stability. To tackle the challenge of mobile robot trajectory tracking under slippery conditions, we propose a hierarchical framework that learns and adapts gains of the tracking controllers simultaneously online. Concretely, a reinforcement learning (RL) module is used to auto-tune parameters in a lateral predictive controller and a longitudinal speed PID controller. Experiments show the necessity of simultaneous gain tuning, and have demonstrated that our online framework outperforms the best baseline controller using fixed gains. By utilizing online gain adaptation, our framework achieves robust tracking performance by rejecting slip and reducing tracking errors when the mobile robot travels through various terrains.

We study the breakup of a liquid thread inside another liquid at different surface tensions. In general, the pinch-off of a liquid thread is governed by the dynamics of fluid flow. However, when the interfacial tension is ultralow (2 to 3 orders lower than normal liquids), we find that the pinch-off dynamics can be governed by bulk diffusion. By studying the velocity and the profile of the pinch-off, we explain why the diffusion-dominated pinch-off takes over the conventional breakup at ultralow surface tensions., Comment: 7 pages, 5 figures. Published version

Due to the complex of mixed spectral point spread function within memory effect range, it is unreliable and slow to use speckle correlation technology for non-invasive imaging through scattering medium under broadband illumination. The contrast of the speckles will drastically drop as the light source's spectrum width increases. Here, we propose a method for producing the optical transfer function with several speckle frames within memory effect range to image under broadband illumination. The method can be applied to image amplitude and color objects under white LED illumination. Compared to other approaches of imaging under broadband illumination, such as deep learning and modified phase retrieval, our method can provide more stable results with faster convergence speed, which can be applied in high speed scattering imaging under natural light illumination.

Topological waveguides have been extensively studied for their robust transmission properties immune to defects and their application potentials for microwave and terahertz integrated circuits. In this work, by using grounded planar valley-Hall photonic topological insulators, a high-efficiency topological directional coupler fed directly by microstrip line with configurable coupling coefficient is theoretically proposed and experimentally demonstrated. The topological directional coupler consists of two coupled topological waveguides, which can be directly integrated with microstrip circuits. Different coupling coefficients were achieved by configuring the coupling between the two topological waveguides. Both simulation and measurement demonstrated the proposed designs. In addition, the proposed design is applicable in both microwave and terahertz bands.

Non-volatile memristors offer a salient platform for artificial neural network (ANN), but the integration of different function blocks into one hardware system remains challenging. Here we demonstrate the implementation of brain-like synaptic (SOT-S) and neuronal (SOT-N) functions in the Bi2Te3/CrTe2 heterostructure-based spin-orbit torque (SOT) device. The SOT-S unit exhibits highly linear (linearity error < 4.19%) and symmetrical long-term potentiation/depression process, resulting in better performance compared to other memristor synapses. Meanwhile, the Sigmoid-shape transition curve inherited in the SOT-N cell replaces the software-based activation function block, hence reducing the system complexity. On this basis, we employ a serial-connected, voltage-mode sensing ANN architecture to enhance the vector-matrix multiplication signal strength with low reading error of 0.61%. Furthermore, the trainable activation function of SOT-N enables the integrated SOT-ANN to execute the Batch Normalization algorithm and activation operation within one clock cycle, which bring about improved on/off-chip training performance close to the ideal baseline.

A new type of polarization sensitive interferometer is proposed, which is named as Delta interferometer due to the geometry of the simplest interferometer looks like Greek letter, Delta. To the best of our knowledge, it is the first time that this type of interferometer is proposed. The main difference between Delta interferometer and other existed interferometer, such as Michelson interferometer, Mach-Zehnder interferometer, Young\rq{}s double-slit interferometer, is that the two interfering paths are asymmetrical in Delta interferometer, which makes it polarization sensitive. The visibility of the first-order interference pattern observed in Delta interferometer is dependent on the polarization of the incidental light. Optical coherence theory is employed to interpret the phenomenon and a single-mode continuous-wave laser is employed to verify the theoretical predictions. The theoretical and experimental results are consistent. Delta interferometer provides a perfect tool to study the reflection of electric field in different polarizations and may find applications in polarization sensitive scenarios.

To alleviate the challenges of building Knowledge Graphs (KG) from scratch, a more general task is to enrich a KG using triples from an open corpus, where the obtained triples contain noisy entities and relations. It is challenging to enrich a KG with newly harvested triples while maintaining the quality of the knowledge representation. This paper proposes a system to refine a KG using information harvested from an additional corpus. To this end, we formulate our task as two coupled sub-tasks, namely join event extraction (JEE) and knowledge graph fusion (KGF). We then propose a Collaborative Knowledge Graph Fusion Framework to allow our sub-tasks to mutually assist one another in an alternating manner. More concretely, the explorer carries out the JEE supervised by both the ground-truth annotation and an existing KG provided by the supervisor. The supervisor then evaluates the triples extracted by the explorer and enriches the KG with those that are highly ranked. To implement this evaluation, we further propose a Translated Relation Alignment Scoring Mechanism to align and translate the extracted triples to the prior KG. Experiments verify that this collaboration can both improve the performance of the JEE and the KGF., Comment: Under review by IEEE Transactions on Knowledge and Data Engineering (TKDE)

Event extraction, the technology that aims to automatically get the structural information from documents, has attracted more and more attention in many fields. Most existing works discuss this issue with the token-level multi-label classification framework by distinguishing the tokens as different roles while ignoring the writing styles of documents. The writing style is a special way of content organizing for documents and it is relative fixed in documents with a special field (e.g. financial, medical documents, etc.). We argue that the writing style contains important clues for judging the roles for tokens and the ignorance of such patterns might lead to the performance degradation for the existing works. To this end, we model the writing style in documents as a distribution of argument roles, i.e., Role-Rank Distribution, and propose an event extraction model with the Role-Rank Distribution based Supervision Mechanism to capture this pattern through the supervised training process of an event extraction task. We compare our model with state-of-the-art methods on several real-world datasets. The empirical results show that our approach outperforms other alternatives with the captured patterns. This verifies the writing style contains valuable information that could improve the performance of the event extraction task., Comment: This paper has been submitted to Pattern Recognition Letters

Stronger light intensity fluctuations are pursued by related applications such as optical resolution, image enhancement, and beam positioning. In this paper, an Nth-order light intensity fluctuation amplifier is proposed, which was demonstrated by a four-wave mixing process with different statistical distribution coupling lights. Firstly, its amplification mechanism is revealed both theoretically and experimentally. The ratio $R$ of statistical distributions and the degree of second-order coherence ${g^{(2)}}(0)$ of beams are used to characterize the affected modulations and the increased light intensity fluctuations through the four-wave mixing process. The results show that the amplification of light intensity fluctuations is caused by not only the fluctuating light fields of incident coupling beams, but also the fluctuating nonlinear coefficient of interaction. At last, we highlight the potentiality of applying such amplifier to other N-order nonlinear optical effects.

Benefit from the promising features of second-order correlation, ghost imaging (GI) has received extensive attentions in recent years. Simultaneously, GI is affected by the poor trade-off between sampling rate and imaging quality. The traditional image reconstruction method in GI is to accumulate the action result of each speckle and the corresponding bucket signal. We found that the image reconstruction process of GI is very similar to the Recurrent Neural Network (RNN), which is one of the deep learning algorithm. In this paper, we proposed a novel method that effectively implements GI on the RNN architecture, called GI-RNN. The state of each layer in RNN is determined by the output of the previous layer and the input of this layer, and the output of the network is the sum of all previous states. Therefore, we take the speckle of each illumination and the corresponding bucket signal as the input of each layer, and the output of the network is the sum of all previous speckle and bucket signal, which is the image of the target. The testing results show that the proposed method can achieve image reconstruction at a very low sampling rate (0.38$\%$). Moreover, we compare GI-RNN with traditional GI algorithm and compressed sensing algorithm. The results of different targets show that GI-RNN is 6.61 dB higher than compressed sensing algorithm and 12.58 dB higher than traditional GI algorithm on average. In our view, the proposed method makes an important step to applications of GI.