###### Abstract  
Many current brain-computer interface (BCI) applications depend on the quick processing of brain signals. Most researchers strive to create new methods for future implementation and enhance existing models to discover an optimal feature set that can operate independently. This study focuses on four key concepts that will be used to complete future works. The first concept is related to potential future communication models, whereas the others aim to enhance previous models or methodologies. The four concepts are as follows. First, we suggest a new communication imagery model as a substitute for a speech imager that relies on a mental task approach. As speech imagery is intricate, one cannot imagine the sounds of every character in every language. Our study proposes a new mental task model for lip-sync imagery that can be employed in all languages. Any character in any language can be used with this mental task model. In this study, we utilized two lip-sync movements to indicate two sounds, characters, or letters. Second, we considered innovative hybrid signals. Choosing an unsuitable frequency range can lead to ineffective feature extractions. Therefore, the selection of an appropriate frequency range is crucial for processing. The ultimate goal of this method is to accurately discover distinct frequencies of brain imagery activities. The restricted frequency range combination presents an initial proposal for generating fragmented, continuous frequencies. The first model assesses two 4 Hz intervals as filter banks. The primary objective is to discover new combinations of signals at 8 Hz by selecting filter banks with a 4 Hz scale from the frequency range of 4 Hz to 40 Hz. This approach facilitates the acquisition of efficient and clearly defined features by reducing similar patterns and enhancing distinctive patterns of brain activity. Third, we introduce a new linear bond graph classifier as a supplement to a linear support vector machine (SVM) when handling noisy data. The performance of the linear support vector machine (SVM) significantly declines under high-noise conditions. To complement the linear support vector machine (SVM) in noisy-data situations, we introduce a new linear bond graph classifier. Fourth, this paper presents a deep-learning model for formula recognition that converts the first-layer data into a formula extraction model. The primary goal is to decrease the noise in the formula coefficients of the subsequent layers. The output of the final layer comprises coefficients chosen by different functions at various levels. The classifier then extracts the root interval for each formula, and a diagnosis is established based on these intervals. The final goal of the last idea is to explain the main brain imagery activity formula using a combination formula for similar and distinctive brain imagery activities. The results of implementing all of the proposed methods are reported. The results range between 55% and 98%. The lowest result is 55% for the deep detection formula, and the highest result is 98% for new combinations of signals.  
speech imagery; mental task; machine learning; feature extraction; common spatial pattern (CSP); filter bank common spatial pattern (FBCSP); brain-computer interface (BCI); principal component analysis (PCA); feature selection; channel selection; mutual information; Lagrange formula; deep learning; SVM classifier