Time-varying discrete cosine transform based on shaping regularization and its application in seismic data analysis

The discrete cosine transform is a commonly used technique in the field of signal processing that employs cosine basis functions for signal analysis. Traditionally, the regression coefficients of the cosine basis functions are solely based on frequency information. This paper extends the regression coefficients associated with the cosine basis functions to take into account both frequency and time information, not just frequency information alone. This modification results in an ill-posed linear system, which requires regularization to prevent overfitting. To address this, this paper uses shaping regularization, a technique used to stabilize ill-posed problems. By doing so, the absolute values of these extended coefficients, now exhibiting variations in both frequency and time domains, are defined as the time-frequency distribution of that input signal. The numerical experiments conducted to validate this approach demonstrate that the proposed method yields a commendable time-frequency resolution. Consequently, it proves valuable for interpreting seismic data, showcasing its potential for applications in this field.