Speech imagery recognition from electroencephalograms (EEGs) could potentially become a strong contender among non-invasive brain-computer interfaces (BCIs). In this report, first we extract language representations as the difference of line-spectra of phones by statistically analyzing many EEG signals from the Broca area. Then we extract vowels by using iterative search from hand-labeled short-syllable data. The iterative search process consists of principal component analysis (PCA) that visualizes linguistic representation of vowels through eigen-vectors φ(m), and subspace method (SM) that searches an optimum line-spectrum for redesigning φ(m). The extracted linguistic representation of Japanese vowels /i/ /e/ /a/ /o/ /u/ shows 2 distinguished spectral peaks (P1, P2) in the upper frequency range. The 5 vowels are aligned on the P1-P2 chart. A 5-vowel recognition experiment using a data set of 5 subjects and a convolutional neural network (CNN) classifier gave a mean accuracy rate of 72.6%.