Coded light
A Wiener filter for equalizing an effect of a first filter on an input signal which is subject to the first filter and to noise and/or interference, wherein: the first filter is dependent on at least one unknown quantity; and the Wiener filter is configured based on an averaged representation of the first filter averaged over the at least one unknown quantity, in place of a representation of the first filter being assumed to be known.
1. A device for processing and/or decoding an input signal, the device comprising:
a camera configured to capture the input signal (X(f)); and
a processor, wherein the processor includes a Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein
the first filter is dependent on at least one unknown quantity;
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known; and
wherein said averaged representation comprises an average of the conjugate of the first filter; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
2. The device of claim 1 , wherein said averaged representation comprises an average of the conjugate of the first filter and an average of: the first filter multiplied by its conjugate.
3. The device of claim 1 , wherein the Wiener filter operates in a frequency domain.
4. The device of claim 3 , wherein the Wiener filter is configured according to:
G
=
E
θ
[
H
*
]
·
S
E
θ
[
HH
*
]
·
S
+
0
where G is a formulation of the Wiener filter in the frequency domain, H is the first filter in the frequency domain, S is a spectral density of the input signal, N 0 is a spectral density of the noise and/or interference, θ is the at least one unknown quantity, and E is the average with respect to θ.
5. The device of claim 1 , wherein the first filter is dependent on a plurality of unknown quantities, and the Wiener filter is configured based on an averaged representation of the first filter averaged over each of said plurality of unknown quantities.
6. The device of claim 1 , wherein the first filter comprises a box function in the time domain and a sinc function in the frequency domain, the box function having a width in the time domain and said plurality of unknown quantities comprising the width of the box function.
7. The device of claim 6 , wherein an exposure of each line produces the box function, whereby each line of a frame is exposed in turn for an exposure time, having a width of the exposure time.
8. The device of claim 1 , wherein the first filter comprises a band pass filter having a center frequency and band width, and said at least one unknown quantity comprises the center frequency and/or band width of the band pass filter.
9. A method of processing and/or decoding an input signal, the method comprising:
capturing, using a camera, the input signal (X(f))));
determining, using a processor, a Wiener filter for equalizing an effect of a first filter on an input signal (X(f)) which is subject to the first filter and to noise and/or interference by, (N(f)),
identifying at least one unknown quantity upon which the first filter is dependent; and
in a formulation of a Wiener filter comprising a representation of the first filter, in place of a representation in which the first filter is assumed to be known, replacing the representation with an averaged representation of the first filter averaged over said at least one unknown quantity;
wherein said averaged representation comprises an average of the conjugate of the first filter; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
10. A non-transitory computer readable medium, configured so as when executed to process and/or decoding an input signal, said medium comprising code to:
capture, using a camera, the input signal (X(f)) by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time;
implement, using processor, a Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known;
wherein said averaged representation comprises an average of the conjugate of the first filter; and
wherein the input signal (X(f)) comprises a coded light signal, the computer program product being configured so as when executed to receive the signal from a rolling shutter acquisition process of a camera whereby each line of a frame is exposed in turn for an exposure time, said filter being a result of the rolling shutter acquisition process and the exposure time being said unknown quantity.
11. A device for processing and/or decoding an input signal, the device comprising:
a camera configured to capture the input signal (X(f)); and
a processor, wherein the processor includes a Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known, wherein said averaged representation comprises an average of: the first filter multiplied by its conjugate; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
12. A device for processing and/or decoding an input signal, the device comprising:
a camera configured to capture the input signal (X(f)); and
a processor, wherein the processor includes a Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known, wherein the averaged representation assumes a uniform distribution of the at least one unknown quantity between finite limits; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
13. A device for processing and/or decoding an input signal, the device comprising:
a camera configured to capture the input signal (X(f)); and
a processor, wherein the processor includes a Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known, wherein the first filter has a nominal value, and said averaging with respect to the at least one unknown quantity is computed using a Taylor series expansion of the first filter around its nominal value and a first plurality of moments of the unknown quantity; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
14. A Wiener filter for equalizing an effect of a first filter on the input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity;
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known;
wherein said averaged representation comprises an average of the conjugate of the first filter; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities.
15. A Wiener filter for equalizing an effect of a first filter on an input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known,
wherein said averaged representation comprises an average of: the first filter multiplied by its conjugate; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities quantity.
16. A Wiener filter for equalizing an effect of a first filter on an input signal (X(f)) which is subject to the first filter and to noise and/or interference (N(f)), wherein:
the first filter is dependent on at least one unknown quantity; and
the Wiener filter is configured based on an averaged representation of the first filter averaged over said at least one unknown quantity, in place of a representation of the first filter being assumed to be known,
wherein the averaged representation assumes a uniform distribution of the at least one unknown quantity between finite limits; and
wherein the input signal (X(f)) comprises a coded light signal captured by a rolling shutter acquisition process whereby each line of a frame is exposed in turn for an exposure time, said Wiener filter being a result of the rolling shutter acquisition process with the exposure time being said plurality of unknown quantities quantity.