Extrapolation for Signal and Image Restoration

Moacir P. Ponti Jr.1, Nelson D. A. Mascarenhas1, Claudio A. T. Suazo2
1Grupo de Arquitetura, Processamento de Imagens e Sinais - GAPIS/DC/UFSCar
2Departamento de Engenharia Química - DEQ/UFSCar

Abstract. Microscopic images, specially with a nonconfocal microscope, are fundamentally limited becaouse the optical transfer function, the Fourier transform of the point-spread function, is zero over a region of the spatial-frequency domain. Several iterative algorithms are being developed for the restoration and superresolution of diffraction-limited imagery data through the use of different mathematical techniques. Here we present the Gerchberg-Papoulis algorithm, test it in a 1-d signal and also in a real microcopic image.

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Microscopic Image from a Cell Culture A 1-d Signal
Original Image Power Spectrum Cutted Signal (to be restored)
Restored Image Power Spectrum FT of the clipped signal
  Setting zero outside the known passband
  Restored signal after IFT