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Compressed sensing is a novel technology that exploits sparsity of a signal to perform sampling below the Nyquist rate, and thus has great potential in low-complexity video sampling and compression applications, due to the significant reduction of the sampling rate ( ) and computational complexity. However, most current work about compressive video sampling (CVS) has focused on real-valued measurements without being quantized, and thus is not applicable to engineering practices. Moreover, in many circumstances, the total number of bits is often constrained. Therefore, how to achieve a compromise between the number of measurements and the number of bits per measurement to maximize the visual quality is a great challenge for CVS, which has still not been addressed in literature. In this paper, we first present a novel distortion model that reveals the relationship between distortion, , and quantization bit-depth ( ). Then, using this model, we propose a joint optimization algorithm, by which we are able to easily derive the values of and . Finally, we present an adaptive and unidirectional CVS framework with rate-distortion (RD) optimized rate allocation, wherein we use video characteristics extracted from partial sampling to allocate the required bits for each block, and then implement "optimized" video sampling and measurement quantization with the estimated and , respectively. Simulation results show that our proposal offers comparable RD performance to the conventional method, with a 4.6 dB improvement in the average PSNR.

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The recently introduced theory of compressed sensing (CS) enables the recovery of sparse or compressible signals from a small set of non-adaptive measurements, and furthermore, it holds promise for substantially improving the performance by leveraging more signal structures that go beyond simple sparsity. In this study, the authors study the weighted l 1 minimisation problem for CS reconstruction when partial support information is available. Firstly, they focus on the coherence-based performance guarantees and show that if an estimated support can be obtained with its accuracy and relative size satisfying certain coherence-related conditions, the weighted l 1 minimisation is then stable and robust under weaker sufficient conditions than that of the analogous standard l 1 optimisation. Meanwhile, better upper bounds on the reconstruction error could also be achieved. Besides, a novel adaptive alternating direction method of multipliers with iterative support detection is outlined to solve the weighted l 1 minimisation problem. Simulation results show that the authors' method achieves good convergence, and obtains improved reconstruction performance in comparison with the conventional methods.

In traditional compressed sensing methods, imposing sparsity alone usually does not produce the most visually pleasing reconstructed videos. Thus, by leveraging more prior information extracted from the temporal redundancy, a regularised reweighted basis pursuit denoising method with estimated support and signal value is proposed for a compressively sampled video. Moreover, an effective alternating direction method of multipliers is presented to solve the optimisation problem. Simulation results show that the proposed method compares favourably with conventional algorithms in the recovery performance.Introduction: Compressed sensing (CS) [1, 2] is an innovative concept that has attracted considerable research interest in the signal processing community. It has wide potential applications in low-complexity video coding, due to the significant reduction of sampling rate, power consumption and computational complexity. In the literature, compressed video sensing can be easily achieved by considering each frame in the sequence independently. However, this simple extension fails to address the temporal redundancy in a video. A straightforward method that does make an effort to exploit the temporal correlation is to treat a three-dimensional (3D) group of frames as a single 1D vector [3]. It reconstructs the video volume by applying a suitable CS reconstruction algorithm using a 3D transform, which incurs a high computation cost. Consequently, the general method for a video is still sampling independently in a frame-by-frame fashion. Then, the remaining challenge is how to utilise the temporal/spatial redundancy in recovering video frames from undersampled measurements. In this Letter, we focus on the design of an efficient reconstruction by leveraging more prior video information that goes beyond simple sparsity, especially when partial support and erroneous pixel values can be obtained.