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... 3D transform; and a similar, yet non-iterative, motion-compensated residual reconstruction. Introduction Recent years have seen significant interest in the paradigm of compressed sensing (CS) (e.g., =-=[1]-=-) which permits, under certain conditions, signals to be sampled at sub-Nyquist rates via linear projection onto a random basis while still enabling exact reconstruction of the original signal. As app...

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...g was investigated for BCSSPL in [3]. Results there demonstrate that BCS-SPL with contourlets or complexvalued wavelets usually matches or exceeds the quality of total-variation reconstruction (e.g., =-=[8]-=-) whose gradient-based operation also promotes smoothing but runs several orders of magnitude slower than SPL algorithm. As a consequence, we adopt the BCS-SPL framework as the core image reconstructi...

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...or example, iterative-thresholding reconstructions start from some initial approximation and form the approximation at each iteration using a specific instance of a projected Landweber (PL) algorithm =-=[7]-=-. PL-based CS reconstruction typically provides reduced computational complexity as compared to pursuits-based reconstruction. Additionally, and perhaps more importantly, the PL formulation offers the...

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...s a consequence, we focus on the case in which each video frame is acquired independently with still-image-based CS sampling, for instance, with successive applications of a single-pixel camera as in =-=[5]-=-. Upon signal recovery, however, the temporal redundancy between successive frames is exploited to improve the reconstruction quality over that of an independent frame-by-frame recovery. In this effor...

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...ionality of the data. Recently, several fast algorithms have been developed for CS reconstruction of generic 1D signals, while the sampling-operator memory challenge was addressed for still images in =-=[2]-=- by using block-based sampling. Additionally in [2], projection-driven Landweber iterations were proposed to accomplish fast reconstruction while simultaneously imposing smoothing with the goal of imp...

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...ed to accomplish fast reconstruction while simultaneously imposing smoothing with the goal of improving the reconstructed-image quality by eliminating blocking artifacts. Subsequent investigations in =-=[3]-=- coupled recent directional transforms with statistically estimated thresholding within the framework introduced in [2]. The term block-based CS (BCS) sampling with smooth projected Landweber (SPL) re...

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...L independently frame-by-frame without capitalizing on frame-to-frame motion. Significant gains are also observed when MC-BCS-SPL is compared to a non-iterative ME/MC-based CS reconstruction of video =-=[6]-=-. CS for a Single Still Image Background Suppose that we want to recover real-valued signal x with length N from M samples, M ≪ N; i.e., we want to recover x from y = Φx, where y has length M, and Φ i...

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...rch 2011, pp. 183–192.would span the entire spatial and temporal extent of a video sequence; however, such global CS sampling of video is largely considered impractical to implement in a real device =-=[4]-=-. As a consequence, we focus on the case in which each video frame is acquired independently with still-image-based CS sampling, for instance, with successive applications of a single-pixel camera as ...