# Seismic Signal Compression Using Nonparametric Bayesian Dictionary Learning via Clustering
## 1 Introduction  
Oil companies are increasing their investment in seismic exploration, as oil is an indispensable resource for economic development. A large number of sensors (typically more than 10,000) are required to collect the seismic signals, which are generated by an active excitation source. Similar to other distributed vibration data collection methods [1; 2], using cable for data transmission in seismic signal acquisitions is a typical approach. To improve the quality of depth images and simplify acquisition logistics, replacing cabling with wireless technology should be a new trend in seismic exploration. Benefitting from recent advances in wireless sensors, large areas could be measured with a dense arrangement of thousands of seismic sensors. This will create high quality of depth images with a large amount of data to be collected daily. However, the network throughput for single sensor is always limited (e.g., 150 kbps down to 50 kbps). Therefore, it is necessary to compress the seismic signals before transmission. How to represent the seismic signals efficiently with a transform or a basis set could be quite important for seismic signal compression. A lossy compression gain of approximately three has been achieved for the compression of seismic signals using the discrete cosine transform (DCT) [3]. To preserve the important features, a two-dimensional seismic-adaptive DCT is proposed [4]. However, complicated signals could not be well represented by the orthogonal basis used in the methods above. Multiscale geometric analysis methods (e.g., Rigielet, Contourlet and Curvelet [5; 6]) have been favored in recent years. By neglecting the orthogonality and completeness, complicated signals could be well represented by inducing a lot of redundancy component. Thereby, the representation of the signals is sparse. For example, Curvelet is adopted in seismic interpretation by exploring the directional features of the seismic data [5]. Another application of Curvelet in seismic signal processing is seismic signal denoising [6]. From a small subset of randomly selected seismic traces, seismic signals are recovered, while noise could be efficiently reduced from the migration amplitudes with the help of sparsity. In the above methods, DCT or Curvelet is used to represent the signals, and could be deemed a set of fixed basis. Recent research efforts have been dedicated to learning a set of adaptive basis, called a dictionary. Hence, the signals could be sparsely represented. The dimensionality of the representation space could be higher than the input space. Moreover, the dictionary is inferred from signals themselves. These two properties lead to an improvement in the sparsity of the representation. Therefore, sparse dictionary learning could be widely used in the fields of compression--especially in image compression applications. An image compression scheme using a recursive least squares dictionary learning algorithm in the 9/7 wavelet domain is proposed [7]. This method is called as a compression method based on Offline Dictionary Learning (OffDL) in this paper. It achieves a better performance than using dictionaries learned by other methods. Reference [8] presents a boosted dictionary learning framework. In this work, an ensemble of complementary specialized dictionaries are constructed for sparse image compression. A compression scheme using dictionary learning and universal trellis coded quantization for complex synthetic aperture radar (SAR) images is proposed in [9], which achieves superior quality of decoded images compared with JPEG, JPEG2000, and CCSDS standards. In the above methods, offline training data is necessary for learning the dictionary for the sparse representation of the online testing data. Thus, its compression performance depends on the correlation between the offline training data and the online testing data. Reference [10] proposes an input-adaptive compression approach. Each input image is coded with a learned dictionary by itself.