This study analyzes bioelectrical signals to achieve automatic epileptic seizure detection. Electroencephalographic (EEG) signals were recorded with electrodes on healthy, epileptic seizure-free, and epileptic seizure patients. The challenges in this field are generally regarded to be the impacts of non-stationarity and nonlinearity in EEG signals. To address these challenges, this study attempts to recognize different brain statuses. The idea originated from a novel hypothesis that considers EEG signals as convolution signals and regards itself as the generation mechanism of EEG signals, to some extent. Based on this hypothesis, the nonlinear problem can be viewed as a deconvolution procedure. As such, the method can be simplified into three parts: eliminating non-stationary is used to catch high-frequency to low-frequency signals, which is followed by a local mean decomposition (LMD) algorithm; these signals are deconvoluted to form ultra-high-dimensional feature sets, which is completely terminated by the mel-frequency cepstrum coefficients (MFCC) algorithm; and several classifiers are combined to achieve highly accurate recognition results and to verify the superiority and reasonableness of this method. The publicly available EEG database from the University of Bonn, Germany is employed to demonstrate the effectiveness and outstanding performance of this method. According to the results, the method has the ability to attain a higher average classification accuracy than other methods in all of the four following cases: healthy (datasets A and B) versus epileptic seizure (dataset E), epileptic seizure-free (datasets C and D) versus epileptic seizure (dataset E), healthy (datasets A and B) versus epileptic seizure-free (datasets C and D) versus epileptic seizure (dataset E), and healthy (dataset A) versus healthy (dataset B) versus epileptic seizure-free (dataset C) versus epileptic seizure-free (dataset D) versus epileptic seizure (dataset E).