Banca de DEFESA: LUCAS ARAUJO DE ALMEIDA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUCAS ARAUJO DE ALMEIDA
DATE: 15/02/2022
TIME: 14:00
LOCAL: Departamento de Eletrônica e Sistemas
TITLE:

LOW COMPLEXITY APPROXIMATIONS FOR DISCRETE HARTLEY TRANSFORM.

KEY WORDS:

Discrete transforms. DHT. Approximate transforms. Hartley. Facial recognition. MACE filters.

PAGES: 88
BIG AREA: Engenharias
AREA: Engenharia Elétrica
SUMMARY:

In recent decades, discrete transforms have received increasing attention with the evolution of digital systems. The signal processing community has focused on developing fast algorithms capable of implementing transforms more efficiently. The extensive research in this area has resulted in algorithms with multiplicative complexity close to the minimum limit. Thus, the approximate transforms emerged as a mathematical tool to avoid multiplication operations. The present dissertation investigates low complexity approximations for a transform with incipient exploration in this sense, the discrete Hartley transform (DHT). Two search methods based on the parameterization of the DHT matrix are proposed and implemented. The first method uses the DHT matrix in its non-factored representation, while the second method makes use of Winograd and Cooley-Tukey factorizations to derive approximations with their fast algorithms. The approximations are obtained by solving an optimization problem that evaluates three objective functions. These functions are metrics of similarity between the approximations and the exact transform. Two of the objective functions are known in the literature, total energy error and orthogonal deviation, and the third metric, called involution error, is proposed in this work. Both search methods derive a total of 45 new approximations of length N = 3, 5, 7, 8, 16, 32. A facial recognition application using MACE filters in Fourier domain was adapted to the Hartley domain. The 18 approximations of length N = 32 obtained were submitted to the face verification system and compared with the exact DHT transform. The approximations presented an average of error rate between 0.32% and 0.50%, some exceeding the exact DHT, which obtained an average of error rate of 0.36%.

BANKING MEMBERS:
Externo ao Programa - 1651445 - RAYDONAL OSPINA MARTINEZ
Interno - 1513566 - RENATO JOSE DE SOBRAL CINTRA
Externo à Instituição - VITOR DE ANDRADE COUTINHO - UFPE