Seismic data ltering with lapped transforms and hidden Markov models

The discrete wavelet transform (DWT) provides sparse bases for natural sig-nal and image processing. DWT is particularly successful for noise removal [1]. Recently, algorithms based on wavelet-domain hidden Markov models (HMMs) have demonstrated excellent performance for image ltering, segmentation and detection [2, 3]. HMM-based algorithms seem to take more advantage of the "clustering" and "persistence " properties of wavelet coeÆcients around image features, such as edges. They enable statistical dependencies modeling and coeÆcients ' non Gaussian behaviour assessment. Wavelets also have recently re-emerged as well as eÆcient compression and noise ltering tools [4] in seismics (originally the eld "wavelets " came from). Some authors have remarked that, although seismic traces usually appear as naturally made of physical wavelets, seismic images are more eÆciently rep-resented by short local bases such as the Local Cosine Transform [5]. Thes