Seismic data denoising and interpolation are essential preprocessing steps in any seismic data processing chain. Sparse transforms with a fixed basis are often used in these two steps. Recently, we have developed an adaptive learning method, the data-driven tight frame (DDTF) method, for seismic data denoising and interpolation. With its adaptability to seismic data, the DDTF method achieves high-quality recovery. For 2D seismic data, the DDTF method is much more efficient than traditional dictionary learning methods. But for 3D or 5D seismic data, the DDTF method results in a high computational expense. The motivation behind this work is to accelerate the filter bank training process in DDTF, while doing less damage to the recovery quality. The most frequently used method involves only a randomly selective subset of the training set. However, this random selection method uses no prior information of the data. We have designed a new patch selection method for DDTF seismic data recovery. We suppose that patches with higher variance contain more information related to complex structures, and should be selected into the training set with higher probability. First, we calculate the variance of all available patches. Then for each patch, a uniformly distributed random number is generated and the patch is preserved if its variance is greater than the random number. Finally, all selected patches are used for filter bank training. We call this procedure the Monte Carlo DDTF method. We have tested the trained filter bank on seismic data denoising and interpolation. Numerical results using this Monte Carlo DDTF method surpass random or regular patch selection DDTF when the sizes of the training sets are the same. We have also used state-of-the-art methods based on the curvelet transform, block matching 4D, and multichannel singular spectrum analysis as comparisons when dealing with field data.