Compressive Sensing for Vision - Sparse Representations and Compressive Sensing for Imaging and Vision - page 49

and rescaling to normalize across all i . These importance weights can be calculated
at each time step without having to perform CS decoding on y .Insomesense,
the filter is acting purely on compressive measurements, and hence the name
”compressive particle filter.”

4.2 Compressive Video Processing

As we saw in the previous sections, recent advances in CS have led to the
development of many imaging devices that sense static signals such as images at
measurement rates lower than the Nyquist rate. Tremendous progress has also been
made in compressively sensing temporal sequences or videos. In this chapter, we
highlight some of these techniques for compressively sensing videos. In particular,
we present an overview of compressive sensing of high-speed periodic videos [147],
programable pixel camera for compressively sensing high speed videos [117] and
compressive acquisition of dynamic scenes [127].

4.2.1 Compressive Sensing for High-Speed Periodic Videos

Processing of periodic signals is an important problem in many applications. For
instance, several human and animal biological processes such as heart-beat, breath-
ing, several cellular processes, industrial automation processes and everyday objects
such as hand-mixer and blender all generate periodic processes. Nevertheless, we
are often unaware of the inner workings of some of these high-speed processes
because they occur at a far greater speed than can be perceived by the human eye.
In [147], a techniques based on compressive sampling was proposed that can turn an
off-the-shelf video camera into a powerful high-speed video camera for observing
periodic events. Essentially, the idea is to capture periodic phenomena by coding
the shutter of a low frame-rate camera during every frame and reconstruct the
phenomena at a higher rate by exploiting sparsity of periodic signals.
Strobing is often used in entertainment, medical imaging and industrial appli-
cations to visualize and capture high-speed visual phenomena. In case of periodic
phenomenon, strobing is commonly used to achieve aliasing and generate lower
beat frequencies. While strobing performs effectively when the scene consists of
a single frequency with a narrow sideband, it is difficult to visualize multiple or
a wider band of frequencies simultaneously. Instead of direct observation of beat
frequencies, one can exploit a computational camera approach based on different
sampling sequences. The key idea is to measure appropriate linear combinations
of the periodic signal and then decode the signal by exploiting the sparsity of
the signal in Fourier domain. Figure 4.4 illustrates the idea behind coded strobing
camera (CSC).