Digital Signal Processing Reference
In-Depth Information
Fig. 2.1
Compressibility of wavelets.
(a)
Original Boats image.
(b)
Wavelet coefficients.
(c)
The
plot of the sorted absolute values of the coefficients.
(d)
Reconstructed image after keeping only
10% of the coefficients with the largest magnitude
2.2
Incoherent Sampling
In CS, the
K
largest
α
i
in (
2.1
) are not measured directly. Instead,
M
N
projections
j
of the vector
x
with a collection of vectors
{
φ
j
}
1
are measured as in
y
j
=
x
,
φ
j
.
=
T
j
Arranging the measurement vector
φ
as rows in an
M
×
N
matrix
Φ
and using
(
2.1
), the measurement process can be written as
y
=
Φ
x
=
Φ
B
α
=
A
α
,
(2.4)
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