Presented

33 Pages·2012·1 MB·English

Compressive Acquisition of
Dynamic Scenes
Authors: Aswin Sankaranarayanan,
Pavan Turaga, Rama Chellappa and
Richard Baraniuk
ECCV 2010, Journal Submission
Presented by: Ajit Rajwade
(May 21, 2012)
Basic Goal of the Paper
• Compressive acquisition of video datasets
• How can you make use of shared information
across frames?
• Challenges: Video data are high-dimensional.
Video data are ephemeral (sudden, non-
smooth changes).
Problem Definition
• To sense a time-varying scene using
compressive measurements of the form
z   y
t t t
Measurements Sensing matrices Original frames
• Given compressive measurements, to
reconstruct the original video frames.
Two Divergent Approaches:
(1) Programmable Pixel Camera (PPC)
• Use full-frame sensory array – during each
exposure of the sensor array, the code at each
pixel is temporally modulated, i.e. addition of full
coded frames across time.
• High temporal multiplexing, but low (or no!)
spatial multiplexing
• References: “Video from a single coded exposure
photograph using a learned overcomplete
dictionary”, Hitomi et al, ICCV 2011.
Two Divergent Approaches:
(2) Single Pixel Camera
• Single Pixel Camera (SPC): a photo-detector obtains a
single (or small number of) measurement(s) per time-
frame, of the form
Measurement vector
(random)
T
z  y
t t t
• High spatial multiplexing, no temporal multiplexing
• SPC is considered more efficient than PPC in cases
where building full-frame sensor array is expensive
(e.g.: infrared wavelengths)
• This paper follows the SPC model.
Video as Linear Dynamical System
(LDS)
•LDS parameterized by matrix pair (C,A) and state
sequence. C and A are time-invariant.
•Choice of C and state sequence unique only up to
invertible d x d linear transformations.
•In this paper, d is much less than N.
LDS for compressive sensing: CS-LDS
• Compressive measurements of the form:
z   y   Cx
t t t t t
• Recover C and state sequence given the
measurements.
Measurement Model
Time-varying
Time-invariant (Common)
measurements
measurements
(Innovation)
Two sets of measurements at
each time instant t
Solving for LDS Parameters
Two Step Procedure:
(1) Estimate the state sequence using
common measurements, i.e.
(2) Given state sequence, estimate
observation matrix C using innovations,
i.e.
(1) Estimating State Sequence
{y },1 t  T
LDS for
t
defined by (C, A)
LDS for 1 t  T
defined by