关键词: 时频峰值滤波, 二维自适应滤波, 凸优化, Adam 算法

Abstract: It is difficult to get a compromise between amplitude protection and denoising by using fixed window
length in TFPF ( Time-Frequency Peak Filtering) Algorithm，and the signal beyond the cut-off frequency can
not be tracked． Moreover，the traditional TFPF only filters along the time direction，ignoring the spatial
information of the signal． To solve these problems，a 2D-ATFPF ( Two-Dimensional Adaptive TFPF) algorithm
is proposed． Firstly，a set of TFPF impulse responses determined by different window functions are used to
construct convex sets of filtering results． Then，an objective function for filtering results is introduced under the
convex set，which is based on the least square criterion and takes the directional derivative with spatiotemporal
correlation as a penalty term． Finally，the optimization of objective function uses a fast convergent projection
Adam method． The application of 2D-ATFPF in synthetic recording and real data show that the new method can
restore the event and the the signal-to-noise ratio has increased about 1． 3 dB compared to the one-dimensional
traditional algorithm．

Key words: time-frequency peak filtering, two-dimensional adaptive filtering, convex optimization,
Adam algorithm