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Theoretical analysis for ℓ 1 - ℓ 2 minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

We investigate the recovery of k -sparse signals using the ℓ 1 - ℓ 2 minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume k -sparse signals 𝐱 with the prior support T which is composed of g true indices and b wrong indices,...

Theoretical foundation of the weighted Laplace inpainting problem

Laurent Hoeltgen, Andreas Kleefeld, Isaac Harris, Michael Breuss (2019)

Applications of Mathematics

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers...

Time-frequency analysis of Sjöstrand's class.

Karlheinz Gröchenig (2006)

Revista Matemática Iberoamericana

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.

Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales.

Loïc Hervé (1996)

Revista Matemática Iberoamericana

We consider quadrature mirror filters, and the associated wavelet packet transform. Let X = {Xn}n∈Z be a stationary signal which has a continuous spectral density f. We prove that the 2n signals obtained from X by n iterations of the transform converge to white noises when n → +∞. If f is holderian, the convergence rate is exponential.

Tropical probability theory and an application to the entropic cone

Rostislav Matveev, Jacobus W. Portegies (2020)

Kybernetika

In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.

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