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Published: 2012

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Compressed sensing is an emerging approach for signal acquisition wherein theory has shown that a small number of linear, random projection of a signal contains enough information for reconstruction of the signal. Despite its potential to enable lightweight and inexpensive sensing hardware that simultaneously combines signal acquisition and dimensionality reduction, the compressed sensing of images and video still entails several challenges, in particular, a sensing-measurement operator which is difficult to apply in practice due to the heavy memory and computational burdens. Block-based random image sampling coupled with a projection-driven compressed-sensing recovery is proposed to address this challenge. For images, the block-based image acquisition is coupled with reconstruction driven by a directional transform and statistical model based thresholding that encourages spatial sparsity. Also considered is an extension of the basic reconstruction algorithm that incorporates block-based measurements in the domain of a wavelet transform. The pro- posed image recovery algorithm and its extension yield images with quality that matches or exceeds that produced by a popular, yet computationally expensive, technique which minimizes total variation with a significantly less computational complexity. For video, motion estimation and compensation is utilized to promote temporal sparsity. A residual between the current frame and the previous frame compensated by object motion is shown to be more sparse than the original frame itself. By using residual reconstruction, information contained in the previous frame contributes to the reconstruction of the current frame. The proposed block-based compressed-sensing reconstruction for video outperforms a simple frame-by-frame reconstruction as well as a 3D volumetric reconstruction in terms of visual quality. Finally, quantization of block-based compressed-sensing measurements is considered in order to generate a true bitstream from a compressed-sensing image acquisition. Specifically, a straightforward process of quantization via simple uniform scalar quantization applied in conjunction with differential pulse code modulation of the block-based compressedsensing measurements is proposed. Experimental results demonstrate significant improvement in rate-distortion performance as compared scalar quantization used alone in several block-based compressed-sensing reconstruction algorithms as well as that of alternative quantized-compressed-sensing techniques relying on optimized quantization or reconstruction is observed.