Estimating a vector x from noisy linear measurements Ax + w often requires use of prior knowledge or structural constraints on x for accurate reconstruction. Several recent works have considered combining linear leas t-squares estimation with a generic or "plug-in" denoiser function that can be des igned in a modular manner based on the prior knowledge about x . While these methods have shown excellent performance, it has been difficult to obtain rigorous performance guarantees. This work considers plug-in denoising combine d with the recently-developed V ector Approximate Message Passing (V AMP) algor ithm, which is itself derived via Expectation Propagation techniques. It shown that the mean squared error of this "plug-and-play" V AMP can be exactly pr edicted for high-dimensional right-rotationally invariant random A and Lipschitz denoisers. The method is demonstrated on applications in image recovery an d parametric bilinear estimation.

As the density of spacecraft in Earth's orbit increases, their recognition, pose and trajectory identification becomes crucial for averting potential collisions and executing debris removal operations. However, training models able to identify a spacecraft and its pose presents a significant challenge due to a lack of available image data for model training. This paper puts forth an innovative framework for generating realistic synthetic datasets of Resident Space Object (RSO) imagery. Using the International Space Station (ISS) as a test case, it goes on to combine image regression with image restoration methodologies to estimate pose from blurred images. An analysis of the proposed image recovery and regression techniques was undertaken, providing insights into the performance, potential enhancements and limitations when applied to real imagery of RSOs. The image recovery approach investigated involves first applying image deconvolution using an effective point spread function, followed by detail object extraction with a U-Net. Interestingly, using only U-Net for image reconstruction the best pose performance was attained, reducing the average Mean Squared Error in image recovery by 97.28% and the average angular error by 71.9%. The successful application of U-Net image restoration combined with the Resnet50 regression network for pose estimation of the International Space Station demonstrates the value of a diverse set of evaluation tools for effective solutions to real-world problems such as the analysis of distant objects in Earth's orbit.

Originality: The paper is mainly based on the idea presented in [14] and could be considered a generalization of it. Section 3.2 is the part which makes this paper's originality clear. Quality: Quality is the issue which makes the reviewer to believe this paper is not ready for publication yet. Here are the issues: - First of all, there are few previous works on the exact same problem that are neither cited nor compared against in this manuscript. These papers even do not need either ground truth data or two sets of measurements (unlike the submitted paper) and have shown impressive results.

The emerging federated learning (FL) [31] has been a great potential to protect data privacy. In FL, the participating devices keep and train their data locally, and only share the trained models (e.g., gradients or parameters), instead of the raw data, with a center server (e.g., cloud). The server updates its global model by aggregating the received device models, and broadcasts the updated global model to all participating devices such that all devices indirectly use all data from other devices. FL has been deployed by many companies such as Google [15], Microsoft [32], IBM [21], Alibaba [2], and applied in various privacy-sensitive applications, including on-device item ranking [31], content suggestions for on-device keyboards [6], next word prediction [27], health monitoring [38], and medical imaging [23]. Unfortunately, recent works show that, though only sharing device models, it is still possible for an adversary (e.g., malicious server) to perform the severe data reconstruction attack (DRA) to FL [57], where an adversary could directly reconstruct the device's training data via the shared device models. Later, a bunch of follow-up enhanced attacks [20, 45, 55, 51, 47, 53, 22, 56, 9, 3, 30, 11, 43, 48, 18, 49, 35]) are proposed by either incorporating (known or unrealistic) prior knowledge or requiring an auxiliary dataset to simulate the training data distribution. However, we note that existing DRA methods have several limitations: First, they are sensitive to the initialization (which is also observed in [47]). For instance, we show in Figure 1 that the attack performance of iDLG [55] and DLG [57] are significantly influenced by initial parameters (i.e., the mean and standard deviation) of a Gaussian distribution, where the initial data is sampled from.

Conventional optimization based methods have utilized forward models with image priors to solve inverse problems in image processing. Recently, deep neural networks (DNN) have been investigated to significantly improve the image quality of the solution for inverse problems. Most DNN based inverse problems have focused on using data-driven image priors with massive amount of data. However, these methods often do not inherit nice properties of conventional approaches using theoretically well-grounded optimization algorithms such as monotone, global convergence. Here we investigate another possibility of using DNN for inverse problems in image processing. We propose methods to use DNNs to seamlessly speed up convergence rates of conventional optimization based methods. Our DNN-incorporated scaled gradient projection methods, without breaking theoretical properties, significantly improved convergence speed over state-of-the-art conventional optimization methods such as ISTA or FISTA in practice for inverse problems such as image inpainting, compressive image recovery with partial Fourier samples, image deblurring, and medical image reconstruction with sparse-view projections.

Estimating a vector $\mathbf{x}$ from noisy linear measurements $\mathbf{Ax+w}$ often requires use of prior knowledge or structural constraints on $\mathbf{x}$ for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or plug-in ``denoiser" function that can be designed in a modular manner based on the prior knowledge about $\mathbf{x}$. While these methods have shown excellent performance, it has been difficult to obtain rigorous performance guarantees. This work considers plug-in denoising combined with the recently-developed Vector Approximate Message Passing (VAMP) algorithm, which is itself derived via Expectation Propagation techniques. It shown that the mean squared error of this ``plug-in" VAMP can be exactly predicted for a large class of high-dimensional random $\Abf$ and denoisers. The method is illustrated in image reconstruction and parametric bilinear estimation.

Solving inverse problems continues to be a central challenge in computer vision. Existing techniques either explicitly construct an inverse mapping using prior knowledge about the corruption, or learn the inverse directly using a large collection of examples. However, in practice, the nature of corruption may be unknown, and thus it is challenging to regularize the problem of inferring a plausible solution. On the other hand, collecting task-specific training data is tedious for known corruptions and impossible for unknown ones. We present MimicGAN, an unsupervised technique to solve general inverse problems based on image priors in the form of generative adversarial networks (GANs). Using a GAN prior, we show that one can reliably recover solutions to underdetermined inverse problems through a surrogate network that learns to mimic the corruption at test time. Our system successively estimates the corruption and the clean image without the need for supervisory training, while outperforming existing baselines in blind image recovery. We also demonstrate that MimicGAN improves upon recent GAN-based defenses against adversarial attacks and represents one of the strongest test-time defenses available today.