5 papers
Samplet limits and multiwavelets
Gianluca Giacchi, Michael Multerer, Jacopo Quizi
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhi…
Metaplectic time-frequency representations
Gianluca Giacchi
Time-frequency representations stemmed in 1932 with the introduction of the Wigner distribution. For most of the 20th century, research in this area primarily focused on defining j…
ALMA: a mathematics-driven approach for determining tuning parameters in generalized LASSO problems, with applications to MRI
Gianluca Giacchi, Isidoros Iakovidis, Bastien Milani +2
Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal…
Boundedness of metaplectic operators within spaces, applications to pseudodifferential calculus, and time-frequency representations
Gianluca Giacchi
Housdorff-Young's inequality establishes the boundedness of the Fourier transform from to spaces for and , where denotes the Lebesgue-conjugat…
Metaplectic Wigner distributions
Gianluca Giacchi
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representati…