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6G operators may use millimeter wave (mmWave) and sub-terahertz (sub-THz) bands to meet the ever-increasing demand for wireless access. Sub-THz communication comes with many existing challenges of mmWave communication and adds new challenges associated with the wider bandwidths, more antennas, and harsher propagations. Notably, the frequency- and spatial-wideband (dual-wideband) effects are significant at sub-THz. This paper presents a compressed training framework to estimate the time-varying sub-THz MIMO-OFDM channels. A set of frequency-dependent array response matrices are constructed, enabling channel recovery from multiple observations across subcarriers via multiple measurement vectors (MMV). Using the temporal correlation, MMV least squares (LS) is designed to estimate the channel based on the previous beam support, and MMV compressed sensing (CS) is applied to the residual signal. We refer to this as the MMV-LS-CS framework. Two-stage (TS) and MMV FISTA-based (M-FISTA) algorithms are proposed for the MMV-LS-CS framework. Leveraging the spreading loss structure, a channel refinement algorithm is proposed to estimate the path coefficients and time delays of the dominant paths. To reduce the computational complexity and enhance the beam resolution, a sequential search method using hierarchical codebooks is developed. Numerical results demonstrate the improved channel estimation accuracy of MMV-LS-CS over state-of-the-art techniques.