Abstract: An inversion-based algorithm for computing the time frequency analysis of reflection seismograms using constrained least-squares spectral analysis is formulated and applied to modeled seismic waveforms and real seismic data. The Fourier series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. Spectra may be provided that have reduced window smearing for a given window length relative to the discrete Fourier transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to the short time Fourier transform and the continuous wavelet transform. The reduction in spectral smoothing enables enhanced determination of spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the short time Fourier transform increases as window length decreases.

Abstract: A method of digital image enhancement and sharpening (11, 12) which may be applied to restoration of blurred digital images of arbitrary origin. The method uses a specially formulated constraint (15) to reconstruct the original images. In particular, the constraint of the present method minimizes the area where strong image parameter variations and discontinuities occur. This new constraint is called a minimum gradient support (MGS) constraint. The MGS constraint generates a stable sharp solution of the linear ill-posed image restoration equation with an arbitrary blurring operator.