Affiliations: [a] Departamento de Sistemas, Universidad Autónoma Metropolitana, Azcapotzalco, México, México | [b] Escuela de Ingeniería y Ciencias, Tecnológico de Monterrey, Atizapán de Zaragoza, México, México | [c] Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Azcapotzalco, México, México
Correspondence:
[*]
Corresponding author. Oscar Herrera-Alcántara, Departamento de Sistemas, Universidad Autónoma Metropolitana, San Pablo 180, Azcapotzalco, 02200, México, México. Tel.: +52 55 5318 9094; Fax: +52 55 5394 4534; E-mail: oha@azc.uam.mx.
Abstract: Inverse parameterizations of length 12 orthogonal wavelet filters are presented, which allow to determine parameter values from filter coefficients. Its applicability is shown in a case of study of image processing where the optimization of five parameters is required. The parameterization of length N filters involves
N2-1
parameters, and it is easier to optimize shorter filters once they explore a subset of the search space. Under this approach, the optimization of length 12 filters is accelerated based on a nested optimization of length 4, 6, 8, and 10 filters by exporting the best solutions from shorter to larger filters via inverse parameterizations. Experimental results support the success of the nested optimization when exploring the search space. The conclusions are that the use of the inverse formulas accelerates the convergence and that parameterized filters provide better results as their length increases and achieve a better performance than standard filters.
