On-the-fly spectral unmixing based on Kalman filtering

This work introduces an on-the-fly (i.e., online) linear unmixing method which is able to sequentially analyze spectral data acquired on a spectrum-by-spectrum basis. After deriving a sequential counterpart of the conventional linear mixing model, the proposed approach recasts the linear unmixing problem into a linear state-space estimation framework. Under Gaussian noise and state models, the estimation of the pure spectra can be efficiently conducted by resorting to Kalman filtering. Interestingly, it is shown that this Kalman filter can operate in a lower-dimensional subspace while ensuring the nonnegativity constraint inherent to pure spectra. This dimensionality reduction allows significantly lightening the computational burden, while leveraging recent advances related to the representation of essential spectral information. The proposed method is evaluated through extensive numerical experiments conducted on synthetic and real Raman data sets. The results show that this Kalman filter-based method offers a convenient trade-off between unmixing accuracy and computational efficiency, which is crucial for operating in an on-the-fly setting. To the best of the authors' knowledge, this is the first operational method which is able to solve the spectral unmixing problem efficiently in a dynamic fashion. It also constitutes a valuable building block for benefiting from acquisition and processing frameworks recently proposed in the microscopy literature, which are motivated by practical issues such as reducing acquisition time and avoiding potential damages being inflicted to photosensitive samples.

Leveraging Self-Supervised Instance Contrastive Learning for Radar Object Detection

In recent years, driven by the need for safer and more autonomous transport systems, the automotive industry has shifted toward integrating a growing number of Advanced Driver Assistance Systems (ADAS). Among the array of sensors employed for object recognition tasks, radar sensors have emerged as a formidable contender due to their abilities in adverse weather conditions or low-light scenarios and their robustness in maintaining consistent performance across diverse environments. However, the small size of radar datasets and the complexity of the labelling of those data limit the performance of radar object detectors. Driven by the promising results of self-supervised learning in computer vision, this paper presents RiCL, an instance contrastive learning framework to pre-train radar object detectors. We propose to exploit the detection from the radar and the temporal information to pre-train the radar object detection model in a self-supervised way using contrastive learning. We aim to pre-train an object detector's backbone, head and neck to learn with fewer data. Experiments on the CARRADA and the RADDet datasets show the effectiveness of our approach in learning generic representations of objects in range-Doppler maps. Notably, our pre-training strategy allows us to use only 20% of the labelled data to reach a similar mAP@0.5 than a supervised approach using the whole training set.

Variational Bayes image restoration with compressive autoencoders

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization of the latent MAP. In this work, we propose to use compressive autoencoders for latent estimation. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. We then introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs this estimation within the framework of variational inference. This allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

A recurrent CNN for online object detection on raw radar frames

Automotive radar sensors provide valuable information for advanced driving assistance systems (ADAS). Radars can reliably estimate the distance to an object and the relative velocity, regardless of weather and light conditions. However, radar sensors suffer from low resolution and huge intra-class variations in the shape of objects. Exploiting the time information (e.g., multiple frames) has been shown to help to capture better the dynamics of objects and, therefore, the variation in the shape of objects. Most temporal radar object detectors use 3D convolutions to learn spatial and temporal information. However, these methods are often non-causal and unsuitable for real-time applications. This work presents RECORD, a new recurrent CNN architecture for online radar object detection. We propose an end-to-end trainable architecture mixing convolutions and ConvLSTMs to learn spatio-temporal dependencies between successive frames. Our model is causal and requires only the past information encoded in the memory of the ConvLSTMs to detect objects. Our experiments show such a method's relevance for detecting objects in different radar representations (range-Doppler, range-angle) and outperform state-of-the-art models on the ROD2021 and CARRADA datasets while being less computationally expensive. The code will be available soon.

Algorithms for audio inpainting based on probabilistic nonnegative matrix factorization

Audio inpainting, i.e., the task of restoring missing or occluded audio signal samples, usually relies on sparse representations or autoregressive modeling. In this paper, we propose to structure the spectrogram with nonnegative matrix factorization (NMF) in a probabilistic framework. First, we treat the missing samples as latent variables, and derive two expectation-maximization algorithms for estimating the parameters of the model, depending on whether we formulate the problem in the time- or time-frequency domain. Then, we treat the missing samples as parameters, and we address this novel problem by deriving an alternating minimization scheme. We assess the potential of these algorithms for the task of restoring short- to middle-length gaps in music signals. Experiments reveal great convergence properties of the proposed methods, as well as competitive performance when compared to state-of-the-art audio inpainting techniques.

Learning the Proximity Operator in Unfolded ADMM for Phase Retrieval

This paper considers the phase retrieval (PR) problem, which aims to reconstruct a signal from phaseless measurements such as magnitude or power spectrograms. PR is generally handled as a minimization problem involving a quadratic loss. Recent works have considered alternative discrepancy measures, such as the Bregman divergences, but it is still challenging to tailor the optimal loss for a given setting. In this paper we propose a novel strategy to automatically learn the optimal metric for PR. We unfold a recently introduced ADMM algorithm into a neural network, and we emphasize that the information about the loss used to formulate the PR problem is conveyed by the proximity operator involved in the ADMM updates. Therefore, we replace this proximity operator with trainable activation functions: learning these in a supervised setting is then equivalent to learning an optimal metric for PR. Experiments conducted with speech signals show that our approach outperforms the baseline ADMM, using a light and interpretable neural architecture.

Regularization via deep generative models: an analysis point of view

This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since the same network can be used for many different problems and experimental conditions, as soon as the generative model is suited to the data. Previous works proposed to use a synthesis framework, where the estimation is performed on the latent vector, the solution being obtained afterwards via the decoder. Instead, we propose an analysis formulation where we directly optimize the image itself and penalize the latent vector. We illustrate the interest of such a formulation by running experiments of inpainting, deblurring and super-resolution. In many cases our technique achieves a clear improvement of the performance and seems to be more robust, in particular with respect to initialization.

Ordinal Non-negative Matrix Factorization for Recommendation

We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender systems, either with explicit data (such as ratings) or implicit data (such as quantized play counts). OrdNMF is a probabilistic latent factor model that generalizes Bernoulli-Poisson factorization (BePoF) and Poisson factorization (PF) applied to binarized data. Contrary to these methods, OrdNMF circumvents binarization and can exploit a more informative representation of the data. We design an efficient variational algorithm based on a suitable model augmentation and related to variational PF. In particular, our algorithm preserves the scalability of PF and can be applied to huge sparse datasets. We report recommendation experiments on explicit and implicit datasets, and show that OrdNMF outperforms BePoF and PF applied to binarized data.

Fast reconstruction of atomic-scale STEM-EELS images from sparse sampling

This paper discusses the reconstruction of partially sampled spectrum-images to accelerate the acquisition in scanning transmission electron microscopy (STEM). The problem of image reconstruction has been widely considered in the literature for many imaging modalities, but only a few attempts handled 3D data such as spectral images acquired by STEM electron energy loss spectroscopy (EELS). Besides, among the methods proposed in the microscopy literature, some are fast but inaccurate while others provide accurate reconstruction but at the price of a high computation burden. Thus none of the proposed reconstruction methods fulfills our expectations in terms of accuracy and computation complexity. In this paper, we propose a fast and accurate reconstruction method suited for atomic-scale EELS. This method is compared to popular solutions such as beta process factor analysis (BPFA) which is used for the first time on STEM-EELS images. Experiments based on real as synthetic data will be conducted.

Hyperspectral and multispectral image fusion under spectrally varying spatial blurs -- Application to high dimensional infrared astronomical imaging

Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low spectral resolution, and hyperspectral images, with low spatial but high spectral resolution. To enhance scientific interpretation of the data, we propose a data fusion method which combines the benefits of each image to recover a high spatio-spectral resolution datacube. The proposed inverse problem accounts for the specificities of astronomical instruments, such as spectrally variant blurs. We provide a fast implementation by solving the problem in the frequency domain and in a low-dimensional subspace to efficiently handle the convolution operators as well as the high dimensionality of the data. We conduct experiments on a realistic synthetic dataset of simulated observation of the upcoming James Webb Space Telescope, and we show that our fusion algorithm outperforms state-of-the-art methods commonly used in remote sensing for Earth observation.