Sur les Theoremes I et II de Painleve

Variantes sur un théorème de Candès, Romberg et Tao

Variations on a theorem of Candès, Romberg and Tao The CRT theorem reconstructs a signal from a sparse set of frequencies, a paradigm of Compressed sensing. The signal is assumed to be carried by a small number of points, s, in a large cyclic set, of order N; the frequencies consist of C s log N points chosen randomly in Z/N Z; the reconstruction is based on a minimal extrapolation in the Wiener algebra of Z/N Z of the restriction of the Fourier transform of the signal to the chosen set of frequencies. The probability of reconstructing the signal is nearly 1 when C is large. The statement shou…