"In recent years, the research focus in signal processing has shifted away from the classical linear paradigm, which is intimately linked with the theory of stationary Gaussian processes. Instead of considering Fourier transforms and performing quadratic optimization, researchers are presently favoring wavelet-like representations and have adopted ”sparsity” as design paradigm.
Our ambition is to develop a unifying operator-based framework for signal processing that would provide the ``sparse"" counterpart of the classical theory, which is currently missing. To that end, we shall specify and investigate sparse stochastic processes that are continuously-defined and ruled by differential equations, and construct corresponding wavelet-like sparsifying transforms. Our hope is to be able to rigorously connect non-quadratic regularization and sparsity-constrained optimization to well-defined continuous-domain statistical models. We also want to develop a novel Lie-group formalism for the design of steerable, signal-adapted wavelet transforms with improved invariance and sparsifying properties, both in 2-D and 3-D.
We shall use these tools to define new reversible image representations in terms of singular points (contours and keypoints) and to develop novel algorithms for 3-D biomedical image analysis. In close collaboration with imaging scientists, we shall apply our framework to the development of new 3-D reconstruction algorithms for emerging bioimaging modalities such as fluorescence deconvolution microscopy, digital holography microscopy, X-ray phase-contrast microscopy, and advanced MRI."
Field of science
- /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations
- /engineering and technology/electrical engineering, electronic engineering, information engineering/electronic engineering/signal processing
Call for proposal
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