Evaluation and applications of the iterated window maximization method for sparse deconvolution

Estimating a sparse signal from a linearly degraded and noisy data record is often desirable in seismic and ultrasonic applications. Bernoulli-Gaussian modeling and maximum a posteriori estimation has proven successful but entails computationally difficult optimization problems that must be solved by suboptimal methods. The iterated window maximization (IWM) algorithm was proposed for such optimization by Kaaresen (see ibid., vol.45, p.1173-83, 1997). The purpose of this paper is twofold. First, the IWM is evaluated against several established alternatives for Bernoulli-Gaussian deconvolution. The restoration quality is quantified by various loss functions, and the average performance is studied through simulation. In all cases examined, the IWM combined better restoration and significantly faster execution than the other algorithms. This motivates extension of IWM to other models, which is the second objective of this paper. Promising real data results are obtained from such diverse applications as robust modeling of ultrasonic nondestructive evaluation data, deblurring of two-dimensional (2-D) astronomical star fields, and segmentation of seismic well logs. It is also argued that IWM can be used for other deconvolution problems as long as the function to be reconstructed is, in some sense, sparse.