2017/10/28 by Naushad Ahmad Ansari, Ansari, Naushad, Anubha Gupta +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Electrical engineering #Image and Signal Denoising Methods #Photoacoustic and Ultrasonic Imaging #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1710.10394
openalex publication_date 2017/10/28 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Transform learning is being extensively applied in several applications\nbecause of its ability to adapt to a class of signals of interest. Often, a\ntransform is learned using a large amount of training data, while only limited\ndata may be available in many applications. Motivated with this, we propose\nwavelet transform learning in the lifting framework for a given signal.\nSignificant contributions of this work are: 1) the existing theory of lifting\nframework of the dyadic wavelet is extended to more generic rational wavelet\ndesign, where dyadic is a special case and 2) the proposed work allows to learn\nrational wavelet transform from a given signal and does not require large\ntraining data. Since it is a signal-matched design, the proposed methodology is\ncalled Signal-Matched Rational Wavelet Transform Learning in the Lifting\nFramework (M-RWTL). The proposed M-RWTL method inherits all the advantages of\nlifting, i.e., the learned rational wavelet transform is always invertible,\nmethod is modular, and the corresponding M-RWTL system can also incorporate\nnonlinear filters, if required. This may enhance the use of RWT in applications\nwhich is so far restricted. M-RWTL is observed to perform better compared to\nstandard wavelet transforms in the applications of compressed sensing based\nsignal reconstruction.\n