Sparse representation is widely used in signal/image reconstruction, denoising, restoration, feature extraction, etc. During data compression most of the low magnitude transform coefficients are thrown away while keeping only the high magnitude coefficients. In some practical applications, data acquisition itself is a major challenge, like, signal acquisition in magnetic resonance imaging (MRI), body area networks (BAN), remote sensing, etc. According to compressed sensing theory if signal/image is sparse in some transform domain and acquired with respect to another basis incoherent to the sparse representation basis then one can reconstruct the underlying signal/image just from a few random projections. Multi-dimensional signal processing involving MRI, BAN and remote sensing images takes significant amount of computational time because of their raw data size. Therefore, state-of-the-art sparse reconstruction algorithms developed for parallel computing with multi-core CPU and GP-GPU is required for realtime or near-realtime implementations.

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多维信号处理中的稀疏表示和压缩感测

稀疏表示广泛用于信号/图像重建，去噪，恢复，特征提取等。在数据压缩期间，大多数低幅度变换系数都被丢弃，而仅保留高幅度系数。在某些实际应用中，数据采集本身就是一个重大挑战，例如磁共振成像（MRI），人体局域网（BAN），遥感等中的信号采集。根据压缩感测理论，如果在某些情况下信号/图像稀疏变换域，并获得与稀疏表示基础不相干的另一基础，然后可以仅从几个随机投影中重建基础信号/图像。涉及MRI的多维信号处理 BAN和遥感图像由于其原始数据大小而需要大量的计算时间。因此，实时或接近实时的实现需要为多核CPU和GP-GPU的并行计算开发的最新的稀疏重建算法。