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High Bit-precision Image Acquisition and
Reconstruction by Planned Sensor Distortion
Pengfei Wan, Oscar C. Au, Jiahao Pang, Ketan Tang, Rui Ma
Department of Electronic and Computer Engineering, HKUST
Abstract
Refinement Algorithm
Figure: Block diagrams of traditional image acquisition (upper figure) and proposed framework (lower figure).
We present a novel framework to acquire high bit-depth images using low bit-depth
quantizers.
Advantages of proposed framework include
1. Simplicity: no change to the core hardware of existing A/D converters
2. Effectiveness: significant PSNR gain over traditional methods
3. Generality: this framework can be applied for acquisition of other analog signals
ˆ p, δ psd, ω, k ∈ {0, 1, 2, 3, · · · }
Input: X
Output: X∗p
1: for all i do
2:
Ni ← (2k + 1) × (2k + 1) neighbors for pixel i
˜i ← {j|j ∈ Ni, (Uj − δ psd(j)) ∩ (Ui − δ psd(i)) 6= ∅}
3:
N
4:
ub∗ ← ∞, lb∗ ← −∞
˜i do
5:
for all j ∈ N
ˆ p(j) + 1 ) · ω − δ psd(j)
6:
ub ← (X
2
ˆ p(j) − 1 ) · ω − δ psd(j)
7:
lb ← (X
2
8:
if ub < ub∗ then
9:
ub∗ ← ub
10:
end if
11:
if lb > lb∗ then
12:
lb∗ ← lb
13:
end if
14:
end for
15:
X∗p(i) ← (ub∗ + lb∗)/2
16: end for
⊲ loop over every pixel
⊲ the useful neighbors
⊲ upper bound
⊲ lower bound
⊲ lowest upper bound
⊲ highest lower bound
⊲ reduced uncertainty
Experiments
Introduction
◮
◮
◮
◮
Facts
◮ Quantization (A/D conversion) → contouring artifacts
◮ High bit-depth quantizers are much more expensive!
Traditional framework that outputs X∗o (Traditional)
Subtractive dithering using pseudo-random noise (Dither)
Proposed framework with random δ psd (Proposed Rand)
Proposed framework with fixed δ psd (Proposed)
Our Goal
◮ increase the bit-depth of acquired signal, without changing the quantizers
Multiple Descriptions (MDs)
◮ Description: a quantized pixel value (representing an uncertainty range)
◮ Traditional method: one description for one pixel value
◮ Proposed method: multiple descriptions for one pixel value!
Assumptions
(a) Traditional, PSNR=21.14dB
(b) Dither, PSNR=20.34dB
(c) Proposed Rand, PSNR=29.09dB
(d) Proposed: PSNR=31.44dB
Combining MDs
◮ If we know the relation between current pixel value X(i) and its neighbor X(j), j ∈ Ni
as: D(i, j) = X(i) − X(j), the uncertainty range for X(i) can be reduced from
ω
ω
ˆ
ˆ
Ui = [X(i) − , X(i) + )
(1)
2
2
to the intersection of several uncertainty ranges:
\
Vi =
{Uj + D(i, j)}
(2)
j∈Ni
◮ length(Vi) ≤ length(Ui) always holds due to the nature of set intersection— we can get
a more accurate estimation of original signal X(i) by combining MDs!
Figure: Reconstructed images in 2-bit quantization (from Kodak dataset).
Markov Assumption
◮ Assumption: D(i, j) ≡ 0 if i and j are adjacent and “X(i) could be equal to X(j))”
Acquisition with Injected δ
psd
D
E
F
D
E
F
G
H
I
G
H
I
J
K
L
J
K
L
D
E
F
D
E
F
G
H
I
G
H
I
J
K
L
J
K
L
(a) Traditional, PSNR=46.71dB
Figure: Reconstructed images in 6-bit quantization (from Tsukuba dataset).
Figure: MDs reduce the length of uncertainty range
Figure: Repeating δ
psd
pattern for 3 × 3
neighborhood. (a, · · · , i) = ω9 (−4, −3, · · · , 4).
◮ Based on our Markov assumption, we intentionally micro-shift the quantizers
◮ Introducing micro-shift δ(i) to a quantizer is equivalent to adding δ psd(i) , −δ(i)
to the original analog signal X(i) before quantization
ˆ p(i) = Q(X(i) + δ psd(i)) instead of Q(X(i))
◮ Our quantized pixel value is X
psd
◮ Adding δ
is an equivalent yet much easier way to misalign quantizers for reducing the
length of uncertainty ranges, while avoiding causing changes to the hardware of ADC.
12
10
PSNR Gain (dB)
(b) micro-shifts: 0, ω2
PSNR Gain (dB)
12
8
6
4
10
8
6
4
2
2
0
0
−2
1
2
3
4
5
Quantizer Bit Depth
(a) Kodak natural images
6
Traditional
Dither
Proposed_Rand
Proposed
14
Traditional
Dither
Proposed_Rand
Proposed
14
(a) no micro-shifts
(b) Proposed: PSNR=54.99dB
7
−2
2
4
6
8
Quantizer Bit Depth
10
(b) New Tsukuba depth images
Figure: Average PSNR gain for both natural images and depth images. X-axis is the quantizer bit-depth; Y-axis
is the PSNR gain over method Traditional.
Contact:
[email protected]