Evaluation of Sequential Importance Sampling for blind deconvolution via a simulation study

Sequential techniques for the canonical blind deconvolution problem have attracted the attention of computational Bayesians such as Liu and Chen (1995) who applied Sequential Importance Sampling (SIS) to this problem. Subsequently, several extensions have been proposed (e.g. Rejuvenation, Rejection Control, Fixed-Lag Smoothing, Metropolis-Hastings Importance Resampling, etc.) as improvements to SIS, but some of the drawbacks inherent in SIS persist. A comparison of variants of the Viterbi (VA), List Viterbi (LVA), BCJR (for Bahl, Cocke, Jelinek and Raviv) and SIS algorithms was conducted with inconclusive results. Although SIS can be helpful in certain circumstances, it shows signs of instability, and therefore, may not be useful in practice. In conclusion, one should be cautious in using SIS or Rejuvenation for blind deconvolution problems.