A Study on Sparse Signal Reconstruction from Interlaced Samples by l1-Norm Minimization

Akira Hirabayashi (1)

1 College of Information Science and Engineering

We propose a sparse signal reconstruction algorithm from interlaced samples with unknown offset parameters based on the l1-norm minimization principle. A typical application of the problem is superresolution from multiple lowresolution images. The algorithm first minimizes the l1-norm of a vector that satisfies data constraint with the offset parameters fixed. Second, the minimum value is further minimized with respect to the parameters. Even though this is a heuristic approach, the computer simulations show that the proposed algorithm perfectly reconstructs sparse signals without failure when the reconstruction functions are polynomials and with more than 99% probability for large dimensional signals when the reconstruction functions are Fourier cosine basis functions.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Akira Hirabayashi. A Study on Sparse Signal Reconstruction from Interlaced Samples by l1-Norm Minimization. SAMPTA-09, May 2009, Marseille, France. pp.Poster session. ⟨hal-00453567⟩