Banca de QUALIFICAÇÃO: VÍTOR SARAIVA RAMOS

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : VÍTOR SARAIVA RAMOS
DATE: 27/12/2022
TIME: 14:30
LOCAL: Videoconferência (https://meet.google.com/nxk-jezr-htv)
TITLE:

Fast Artifact-Free Optimum Histogram Specification.

KEY WORDS:

Algorithms, data preprocessing, data processing, histograms, optimization, sorting.

PAGES: 40
BIG AREA: Engenharias
AREA: Engenharia Elétrica
SUMMARY:

In this work, we propose two novel algorithms for histogram specification and quantile transformation of data without local information, two techniques that serve as building blocks for applications that require the specification of the sample distribution of a data set. Histogram specification is best known for its image enhancement applications, whereas quantile transformation is typically employed in data preprocessing for data normalization. In signal processing, histogram specification methods often require temporal or spatial information; in data preprocessing, quantile transformation methods work by interpolation or by approximation, drawing from results in computational statistics, and have a trade-off between speed and quality. It is nontrivial to accommodate for cases that do not have local information (e.g., tabular data) while also providing a fast, exact solution. For that, we take up a concept in image processing called group mapping law and propose an extension. The proposed extension allows us to formulate a convex functional where we look for the best approximation between the output unique values and the reference histogram. Then, we apply the ordered assignment solution, a result in optimal transport, to reconstruct the output from the optimal unique values. Two sets of results show the effectiveness of the proposed algorithms when compared to traditional and state-of-the-art methods. The proposed algorithms are fast, exact, and at least p-norm optimal. Further, we define the algorithms as generic data processing methods. Thus, our contributions can be easily incorporated in applications spanning many disciplines, especially in applied data sciences.

COMMITTEE MEMBERS:
Presidente - 1543191 - LUIZ FELIPE DE QUEIROZ SILVEIRA
Externo ao Programa - 1668928 - LUIZ GONZAGA DE QUEIROZ SILVEIRA JUNIOR - UFRNExterno ao Programa - 2929823 - RAFAEL BESERRA GOMES - UFRN