João F. C. Mota

João F. C. Mota, João M. F. Xavier, Pedro M. Q. Aguiar et al. · eth-zurich

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time. We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes. Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multipliers. We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms.

Rahul Mourya, João F. C. Mota

End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline and often fail to reconstruct small but important details, a feature critical in medical imaging, astronomy, or defence. Such instabilities in DNNs can be explained by the fact that they ignore the forward measurement model during deployment, and thus fail to enforce consistency between their output and the input measurements. To overcome this, we propose a framework that transforms any DNN for inverse problems into a measurement-consistent one. This is done by appending to it an implicit layer (or deep equilibrium network) designed to solve a model-based optimization problem. The implicit layer consists of a shallow learnable network that can be integrated into the end-to-end training while keeping the SOTA DNN fixed. Experiments on single-image super-resolution show that the proposed framework leads to significant improvements in reconstruction quality and robustness over the SOTA DNNs.

Yining Ding, João F. C. Mota, Andrew M. Wallace et al.

We propose a method which, given a sequence of stereo foggy images, estimates the parameters of a fog model and updates them dynamically. In contrast with previous approaches, which estimate the parameters sequentially and thus are prone to error propagation, our algorithm estimates all the parameters simultaneously by solving a novel optimisation problem. By assuming that fog is only locally homogeneous, our method effectively handles real-world fog, which is often globally inhomogeneous. The proposed algorithm can be easily used as an add-on module in existing visual Simultaneous Localisation and Mapping (SLAM) or odometry systems in the presence of fog. In order to assess our method, we also created a new dataset, the Stereo Driving In Real Fog (SDIRF), consisting of high-quality, consecutive stereo frames of real, foggy road scenes under a variety of visibility conditions, totalling over 40 minutes and 34k frames. As a first-of-its-kind, SDIRF contains the camera's photometric parameters calibrated in a lab environment, which is a prerequisite for correctly applying the atmospheric scattering model to foggy images. The dataset also includes the counterpart clear data of the same routes recorded in overcast weather, which is useful for companion work in image defogging and depth reconstruction. We conducted extensive experiments using both synthetic foggy data and real foggy sequences from SDIRF to demonstrate the superiority of the proposed algorithm over prior methods. Our method not only produces the most accurate estimates on synthetic data, but also adapts better to real fog. We make our code and SDIRF publicly available\footnote{https://github.com/SenseRoboticsLab/estimating-fog-parameters} to the community with the aim of advancing the research on visual perception in fog.

Junli Fang, João F. C. Mota, Baoshan Lu et al.

The joint source-channel coding (JSCC) framework leverages deep learning to learn from data the best codes for source and channel coding. When the output signal, rather than being binary, is directly mapped onto the IQ domain (complex-valued), we call the resulting framework joint source coding and modulation (JSCM). We consider a JSCM scenario and show the existence of a strict tradeoff between channel rate, distortion, perception, and classification accuracy, a tradeoff that we name RDPC. We then propose two image compression methods to navigate that tradeoff: the RDPCO algorithm which, under simple assumptions, directly solves the optimization problem characterizing the tradeoff, and an algorithm based on an inverse-domain generative adversarial network (ID-GAN), which is more general and achieves extreme compression. Simulation results corroborate the theoretical findings, showing that both algorithms exhibit the RDPC tradeoff. They also demonstrate that the proposed ID-GAN algorithm effectively balances image distortion, perception, and classification accuracy, and significantly outperforms traditional separation-based methods and recent deep JSCM architectures in terms of one or more of these metrics.

Marija Vella, Bowen Zhang, Wei Chen et al.

Hyperspectral (HS) images contain detailed spectral information that has proven crucial in applications like remote sensing, surveillance, and astronomy. However, because of hardware limitations of HS cameras, the captured images have low spatial resolution. To improve them, the low-resolution hyperspectral images are fused with conventional high-resolution RGB images via a technique known as fusion based HS image super-resolution. Currently, the best performance in this task is achieved by deep learning (DL) methods. Such methods, however, cannot guarantee that the input measurements are satisfied in the recovered image, since the learned parameters by the network are applied to every test image. Conversely, model-based algorithms can typically guarantee such measurement consistency. Inspired by these observations, we propose a framework that integrates learning and model based methods. Experimental results show that our method produces images of superior spatial and spectral resolution compared to the current leading methods, whether model- or DL-based.

Marija Vella, João F. C. Mota

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images. In these applications, DNNs invert a forward operator by finding, via training data, a map between the measurements and the input images. It is then expected that the map is still valid for the test data. This framework, however, introduces measurement inconsistency during testing. We show that such inconsistency, which can be critical in domains like medical imaging or defense, is intimately related to the generalization error. We then propose a framework that post-processes the output of DNNs with an optimization algorithm that enforces measurement consistency. Experiments on MR images show that enforcing measurement consistency via our method can lead to large gains in reconstruction performance.

Marija Vella, João F. C. Mota

Single-image super-resolution is the process of increasing the resolution of an image, obtaining a high-resolution (HR) image from a low-resolution (LR) one. By leveraging large training datasets, convolutional neural networks (CNNs) currently achieve the state-of-the-art performance in this task. Yet, during testing/deployment, they fail to enforce consistency between the HR and LR images: if we downsample the output HR image, it never matches its LR input. Based on this observation, we propose to post-process the CNN outputs with an optimization problem that we call TV-TV minimization, which enforces consistency. As our extensive experiments show, such post-processing not only improves the quality of the images, in terms of PSNR and SSIM, but also makes the super-resolution task robust to operator mismatch, i.e., when the true downsampling operator is different from the one used to create the training dataset.

Marija Vella, João F. C. Mota

Super-resolution (SR) is a technique that allows increasing the resolution of a given image. Having applications in many areas, from medical imaging to consumer electronics, several SR methods have been proposed. Currently, the best performing methods are based on convolutional neural networks (CNNs) and require extensive datasets for training. However, at test time, they fail to impose consistency between the super-resolved image and the given low-resolution image, a property that classic reconstruction-based algorithms naturally enforce in spite of having poorer performance. Motivated by this observation, we propose a new framework that joins both approaches and produces images with superior quality than any of the prior methods. Although our framework requires additional computation, our experiments on Set5, Set14, and BSD100 show that it systematically produces images with better peak signal to noise ratio (PSNR) and structural similarity (SSIM) than the current state-of-the-art CNN architectures for SR.

Pingfan Song, Xin Deng, João F. C. Mota et al.

Real-world data processing problems often involve various image modalities associated with a certain scene, including RGB images, infrared images or multi-spectral images. The fact that different image modalities often share certain attributes, such as certain edges, textures and other structure primitives, represents an opportunity to enhance various image processing tasks. This paper proposes a new approach to construct a high-resolution (HR) version of a low-resolution (LR) image given another HR image modality as reference, based on joint sparse representations induced by coupled dictionaries. Our approach, which captures the similarities and disparities between different image modalities in a learned sparse feature domain in \emph{lieu} of the original image domain, consists of two phases. The coupled dictionary learning phase is used to learn a set of dictionaries that couple different image modalities in the sparse feature domain given a set of training data. In turn, the coupled super-resolution phase leverages such coupled dictionaries to construct a HR version of the LR target image given another related image modality. One of the merits of our sparsity-driven approach relates to the fact that it overcomes drawbacks such as the texture copying artifacts commonly resulting from inconsistency between the guidance and target images. Experiments on real multimodal images demonstrate that incorporating appropriate guidance information via joint sparse representation induced by coupled dictionary learning brings notable benefits in the super-resolution task with respect to the state-of-the-art. Of particular relevance, the proposed approach also demonstrates better robustness than competing deep-learning-based methods in the presence of noise.

Nikos Deligiannis, João F. C. Mota, Bruno Cornelis et al.

In support of art investigation, we propose a new source sepa- ration method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation meth- ods, which are based on statistical or structural incoherence of the sources, we use visual images taken from the front- and back-side of the panel to drive the separation process. The coupling of the two imaging modalities is achieved via a new multi-scale dictionary learning method. Experimental results demonstrate that our method succeeds in the discrimination of the sources, while state-of-the-art methods fail to do so.

João F. C. Mota, Nikos Deligiannis, Miguel R. D. Rodrigues

We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1 and L1-L2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced via L1-L1 minimization, but not so much via L1-L2 minimization. We provide geometrical interpretations and experimental results illustrating our findings.