Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon-Nyquist sampling theorem, whereas compressive sensing (CS) provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm (SPGL1), and ten different random seeds. According to the signal-to-noise ratio (SNR) between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes.

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In transform domain distributed video coding scheme, we found that there was a certain deviation between Laplacian statistical distribution and the distribution of small and large residual coefficients. To reduce this deviation, this paper proposes a hybrid distribution correlation noise model (HDCNM) based on K-Mediods, which models small coefficients as improved Laplacian distribution while modeling large ones as Cauchy distribution. The parameter estimation algorithm is also given. The experimental results show that the hybrid model proposed in this paper can describe the distribution of residual coefficients between WZ frame and side information accurately, so as to improve the distortion performance of transform domain distributed video coding effectively, and reduce the computational complexity of decoder.

In the light of the high decoding complexity and large transmission delay caused by the bit rate allocation of Distributed Video Coding (DVC) scheme with feedback channel, this paper proposes an improved bit rate control algorithm without feedback. The algorithm uses the division of macro block to simplify the bit rate allocation, and switches Laplacian parameters in the Correlation Noise Model (CNM) between the block-level and frame-level to adjust rate based on the intensity of motion. The simulation results show that the proposed algorithm can accurately control coding bit rate and transmission delay only at the cost of a small amount of coding complexity, and effectively guarantee the rate-distortion performance of DVC system.