Sparsity Properties of Compressive Video Sampling Generated by Coefficient Thresholding

        The fact is signals in nature have an internal structure that can be exploited greatly, it
is not ussually that we are able to compress those signals to some extent so that the
recovery still acquires acceptable accuracy. According with this, the compressive sensing/sampling
is a relatively new paradigm in signal processing, where the sampling frequency might be lower
than that of the Nyquist theorem  requirement. The acquisition phase is very simple and
integrated with the compression phase, as the name implies. And next, compressive video
sampling is one of the promising applications of CS due to its demand on the low complexity
encoding process. The consequence of this is the simple acquisition, the reconstruction phase is quite
complicated yet computationally feasible.
        The ability of compressive sampling to be implemented in
a video coding framework. However, it did not consider motion compensation to reduce
temporal redundancy by exploiting inter-frame correlation. Other works related to compressive
video sampling. The former method focused on video processing and
reconstuction of multiple frames simultaneously  rather than forming smaller blocks, while the
later studied distributed video coding, in which the coder conducted conventional sampling for
reference or key frames and compressive sampling for non reference frames. The application of
compressive video sampling in multimedia communication such as wireless visual sensornetworks (WVSN), while single pixel camera application for earth observation.
The Nyquist Shannon limit finally can be broke by the CS method by taking fewer measurements for
exact recovery, as long as the signal is adequately sparse and the random matrices are
incoherent to each other. Various algorithms have been proposed to reconstruct highly
incomplete signals. These algorithms are categorized into three classes, i.e. convex
optimization, greedy algorithm, and iterative thresholding. In this research, we use the convex
optimization represented by basis pursuit (BP).
       As on the theoretically, basis pursuit should outperform matching pursuit (MP) in terms of accuracy. On the other hand, MP might be less complex and have faster processing time. In general, the basis pursuit method will reconstruct the optimum signal by means of linear programming. The received signal will be decomposed into smaller parts from an over-complete dictionary. The decision on which element must be
selected is resulted from the calculation of L1 norm.

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