Software developed by our team can be found here.
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We are currently designing novel reinforcement-learning (RL) algorithms for continuous and high-dimensional state/action spaces.
We do not follow standard routes, but we introduce novel Bellman mappings which sample the state space on-the-fly, require no information on transition probabilities of Markov decision processes, and may operate with no training data available. In contrast to the prevailing line of research, which defines Bellman mappings in $\mathcal{L}_{\infty}$-norm Banach spaces (no inner product available by definition), our Bellman mappings are designed specifically for reproducing kernel Hilbert spaces (RKHSs) to capitalize on their geometry and rich properties of their inner products.
See, for example, our papers in IEEE Transactions on Signal Processing and arXiv.
We also introduce new ways to model Q-function losses via Gaussian-mixture-models and Riemannian optimization. Results on these novel directions will be reported at several publication venues.
See, for example, our preprint in arXiv.

We study sparse optimization, which aims to estimate solutions with sparsity—vectors whose most of their entries are zero. Such sparse representation is particularly useful when only a limited subset of data or features is important, as is the case with high-dimensional data. Applications include compressive sensing, feature selection, audio and image processing, etc.
A basic problem in sparse optimization is to estimate a sparse signal/vector $\mathbf{x}$ from measurements modeled as $\mathbf{y} = \mathbf{Ax} + \mathbf{n}$, where $\mathbf{n}$ is Gaussian noise. A standard approach is to minimize a cost function composed of a quadratic loss term and a sparsity-inducing penalty term. One of the most widely used methods is LASSO, which employs the $\mathcal{L}_1$-norm penalty. However, the $\mathcal{L}_1$ norm is known to cause estimation bias. To address this issue, the so-called Moreau-enhancement technique has recently received significant attention. See, for example, reference 1, reference 2, and reference 3.
To this end, we proposed a robust sparse signal recovery method by exploiting an effective way of utilizing Moreau enhancement, see [IEEE Transactions on Signal Processing]. We further introduced the new notion of “external division operator,” which extends the idea of Moreau enhancement, see [IEEE ICASSP 2024]. More results on this new direction will be reported in future publications.

We study learning with low-dimensional manifolds. Manifolds are smooth surfaces typically embedded in high-dimensional spaces, providing a structured and rigorous framework to identify latent patterns and data structures.
Our starting point is regression. We introduce a novel non-parametric regression framework that requires only the assumption of manifold smoothness. Neither explicit knowledge of the manifold nor training data is necessary to perform regression tasks. The framework integrates naturally with reproducing kernel Hilbert space methods—a well-established functional approximation toolbox—and accommodates data with missing entries. We validate our approaches on dynamic MRI, where data imputation is needed, and graph signal processing, where edge-flow estimation is essential.
Take a look, for example, at our papers in IEEE Open Journal of Signal Processing, IEEE Transactions on Computational Imaging and IEEE Transactions on Medical Imaging.
We also develop methods to learn from manifolds with explicit geometric structure, such as Riemannian manifolds. We introduce novel data approximation methods and validate our approaches across multiple application domains, including fMRI and graph signal processing. Current extensions accommodate tensor/multi-way data.
See, for example, our paper in arXiv.

We develop quantum computing methods and quantum-inspired algorithms for signal processing and machine learning.
As an example of our quantum-inspired direction, we design trainable tensor-network circuits inspired by quantum computing principles and apply them to image reconstruction from partial observations—called image inpainting.
When an observed image has missing pixels, the full-resolution image can usually be recovered by assuming it exhibits some structure—prior knowledge—in a suitable transform domain. For example, sparsity is exploited in a wavelet-basis domain, while other transforms may encode different structural properties. However, not all transforms work equally well with randomly sampled pixels. A fundamental trade-off exists: transforms that effectively capture image structure may concentrate information in small image-domain regions, making it easy to miss important data when pixels are sampled.
Our trainable quantum-inspired tensor-network circuits adapt to image structure while maintaining a mathematical property (low coherence) that yields good inpainting performance. The method trains efficiently using standard optimization without specialized geometry, yet achieves performance exceeding classical transforms and state-of-the-art learning methods while using far fewer parameters. This work—see our arXiv paper—demonstrates how quantum-inspired structural principles can lead to efficient, theoretically grounded algorithms for practical signal processing tasks.

We study here the case of learning from data/features which live in Riemannian manifolds; a special class of manifolds endowed with an inner product and thus a distance metric.
These concepts may appear abstract, but they give us the freedom to employ our geometric intuition to address learning tasks in a wide variety of application domains. For example, numerous well-known features in signal processing and machine learning belong to Riemannian manifolds; see correlation matrices, orthogonal matrices, fixed-rank linear subspaces and tensors, probability density functions, etc.
With regards to applications, we consider the basic learning tasks of clustering and classification on data taken from network time series, and in particular, from brain networks. Several research directions are currently under study.
See, for example, our papers in IEEE Open Journal of Signal Processing and Signal Processing.