In this paper, we aimed to separate the 1/f noise from the original signal, and analyzed its characteristics of power spectrum. First, an N-level wavelet transform has been applied to the original data signal before the compressed sensing observation for the original signal. Compared with the tradition measurement procession of compressed sensing, the measurement matrix here is replaced with the circulant matrix. This can greatly reduce the measurement number compared with the random Gaussian matrix. To reduce the algorithm time, some zero independent elements are introduced to the circulant matrix. This proposed circulant matrix is then helpful to save 60 percent of algorithm’s reconstruction time.
This paper presents a parallel algorithm designed for 1/f noise signal estimation based on Compressed sensing theory on the GPU platform. In the accelerating process, we select parts of the serial program as the object to be speeded up for the execution time of algorithm. Compared with the conventional methods for 1/f noise estimation, our scheme has shown a 20x speedup.