Sparse representations have been the key underpinning ingredients of statistical learning in signal and image processing. They enable the design of very powerful non-linear algorithms based on statistical assumptions that depart significantly from those of Gaussianity and stationarity. Over time, my group has contributed numerous such algorithms, which offer state-of-the-art performance in the analysis of digital images, multiresolution algorithms, image denoising and fusion, segmentation and classification, and image super-resolution. We have unique expertise in image processing algorithms using sparse distributions in sparse domains and their application to various imaging modalities.

In the current era of ML and AI, I did not give up on my life-long quest for designing better solutions to inverse problems by exploiting the statistical characteristics of the data, but chose instead to adapt my interests to the new trends. Specifically, I have been investigating methods that combine classical model-based approaches with data-driven techniques, while at the same time investing a considerable amount of effort in characterizing theoretically novel penalty functions. These can be used as building blocks for various deep learning architectures, either as loss functions, or directly for the design of new representation learning architectures that exploit the statistical sparsity of the input data while enforcing classical sparsity on the learnt representations.

From an applications perspective, my research focusses primarily on two apparently very different domains but with a surprisingly high number of synergies and linked together via core fundamental research on computational imaging and statistical machine learning. These are Earth Observation, mainly via Synthetic Aperture Radar, and medical and biological imaging.