title: Source Modulated Multiplexed Hyperspectral Imaging: Theory, Hardware and Application

authors: Streeter, Lee

subjects: Hadamard transform

abstract: The design, analysis and application of a multiplexing hyperspectral imager is presented.
The hyperspectral imager consists of a broadband digital light projector that uses a digital
micromirror array as the optical engine to project light patterns onto a sample object. A
single point spectrometer measures light that is reflected from the sample. Multiplexing
patterns encode the spectral response from the sample, where each spectrum taken is the
sum of a set of spectral responses from a number of pixels. Decoding in software recovers
the spectral response of each pixel. A technique, which we call complement encoding, is
introduced for the removal of background light effects. Complement encoding requires
the use of multiplexing matrices with positive and negative entries.
The theory of multiplexing using the Hadamard matrices is developed. Results from
prior art are incorporated into a singular notational system under which the different
Hadamard matrices are compared with each other and with acquisition of data without
multiplexing (pointwise acquisition). The link between Hadamard matrices with strongly
regular graphs is extended to incorporate all three types of Hadamard matrices. The effect
of the number of measurements used in compressed sensing on measurement precision is
derived by inference using results concerning the eigenvalues of large random matrices.
The literature shows that more measurements increases accuracy of reconstruction. In
contrast we find that more measurement reduces precision, so there is a tradeoff between
precision and accuracy. The effect of error in the reference on the Wilcoxon statistic is
derived. Reference error reduces the estimate of the Wilcoxon, however given an estimate
of theWilcoxon and the proportion of error in the reference, we show thatWilcoxon
without error can be estimated.
Imaging of simple objects and signal to noise ratio (SNR) experiments are used to
test the hyperspectral imager. The simple objects allow us to see that the imager produces
sensible spectra. The experiments involve looking at the SNR itself and the SNR boost,
that is ratio of the SNR from multiplexing to the SNR from pointwise acquisition. The
SNR boost varies dramatically across the spectral domain from 3 to the theoretical maximum
of 16. The range of boost values is due to the relative Poisson to additive noise
variance changing over the spectral domain, an effect that is due to the light bulb output
and detector sensitivity not being flat over the spectral domain. It is shown that the SNR boost is least where the SNR is high and is greatest where the SNR is least, so the boost
is provided where it is needed most. The varying SNR boost is interpreted as a preferential
boost, that is useful when the dominant noise source is indeterminate or varying.
Compressed sensing precision is compared with the accuracy in reconstruction and with
the precision in Hadamard multiplexing. A tradeoff is observed between accuracy and
precision as the number of measurements increases. Generally Hadamard multiplexing is
found to be superior to compressed sensing, but compressed sensing is considered suitable
when shortened data acquisition time is important and poorer data quality is acceptable.
To further show the use of the hyperspectral imager, volumetric mapping and analysis
of beef m. longissimus dorsi are performed. Hyperspectral images are taken of successive
slices down the length of the muscle. Classification of the spectra according to visible
content as lean or nonlean is trialled, resulting in a Wilcoxon value greater than 0.95,
indicating very strong classification power. Analysis of the variation in the spectra down
the length of the muscles is performed using variography. The variation in spectra of a
muscle is small but increases with distance, and there is a periodic effect possibly due to
water seepage from where connective tissue is removed from the meat while cutting from
the carcass. The spectra are compared to parameters concerning the rate and value of
meat bloom (change of colour post slicing), pH and tenderometry reading (shear force).
Mixed results for prediction of blooming parameters are obtained, pH shows strong correlation (R² = 0.797) with the spectral band 598-949 nm despite the narrow range of
pH readings obtained. A likewise narrow range of tenderometry readings resulted in no
useful correlation with the spectra.
Overall the spatial multiplexed imaging with a DMA based light modulation is successful.
The theoretical analysis of multiplexing gives a general description of the system
performance, particularly for multiplexing with the Hadamard matrices. Experiments
show that the Hadamard multiplexing technique improves the SNR of spectra taken over
pointwise imaging. Aspects of the theoretical analysis are demonstrated. Hyperspectral
images are acquired and analysed that demonstrate that the spectra acquired are sensible
and useful.

text: Source Modulated Multiplexed Hyperspectral Imaging: Theory, Hardware and Application The design, analysis and application of a multiplexing hyperspectral imager is presented.
The hyperspectral imager consists of a broadband digital light projector that uses a digital
micromirror array as the optical engine to project light patterns onto a sample object. A
single point spectrometer measures light that is reflected from the sample. Multiplexing
patterns encode the spectral response from the sample, where each spectrum taken is the
sum of a set of spectral responses from a number of pixels. Decoding in software recovers
the spectral response of each pixel. A technique, which we call complement encoding, is
introduced for the removal of background light effects. Complement encoding requires
the use of multiplexing matrices with positive and negative entries.
The theory of multiplexing using the Hadamard matrices is developed. Results from
prior art are incorporated into a singular notational system under which the different
Hadamard matrices are compared with each other and with acquisition of data without
multiplexing (pointwise acquisition). The link between Hadamard matrices with strongly
regular graphs is extended to incorporate all three types of Hadamard matrices. The effect
of the number of measurements used in compressed sensing on measurement precision is
derived by inference using results concerning the eigenvalues of large random matrices.
The literature shows that more measurements increases accuracy of reconstruction. In
contrast we find that more measurement reduces precision, so there is a tradeoff between
precision and accuracy. The effect of error in the reference on the Wilcoxon statistic is
derived. Reference error reduces the estimate of the Wilcoxon, however given an estimate
of theWilcoxon and the proportion of error in the reference, we show thatWilcoxon
without error can be estimated.
Imaging of simple objects and signal to noise ratio (SNR) experiments are used to
test the hyperspectral imager. The simple objects allow us to see that the imager produces
sensible spectra. The experiments involve looking at the SNR itself and the SNR boost,
that is ratio of the SNR from multiplexing to the SNR from pointwise acquisition. The
SNR boost varies dramatically across the spectral domain from 3 to the theoretical maximum
of 16. The range of boost values is due to the relative Poisson to additive noise
variance changing over the spectral domain, an effect that is due to the light bulb output
and detector sensitivity not being flat over the spectral domain. It is shown that the SNR boost is least where the SNR is high and is greatest where the SNR is least, so the boost
is provided where it is needed most. The varying SNR boost is interpreted as a preferential
boost, that is useful when the dominant noise source is indeterminate or varying.
Compressed sensing precision is compared with the accuracy in reconstruction and with
the precision in Hadamard multiplexing. A tradeoff is observed between accuracy and
precision as the number of measurements increases. Generally Hadamard multiplexing is
found to be superior to compressed sensing, but compressed sensing is considered suitable
when shortened data acquisition time is important and poorer data quality is acceptable.
To further show the use of the hyperspectral imager, volumetric mapping and analysis
of beef m. longissimus dorsi are performed. Hyperspectral images are taken of successive
slices down the length of the muscle. Classification of the spectra according to visible
content as lean or nonlean is trialled, resulting in a Wilcoxon value greater than 0.95,
indicating very strong classification power. Analysis of the variation in the spectra down
the length of the muscles is performed using variography. The variation in spectra of a
muscle is small but increases with distance, and there is a periodic effect possibly due to
water seepage from where connective tissue is removed from the meat while cutting from
the carcass. The spectra are compared to parameters concerning the rate and value of
meat bloom (change of colour post slicing), pH and tenderometry reading (shear force).
Mixed results for prediction of blooming parameters are obtained, pH shows strong correlation (R² = 0.797) with the spectral band 598-949 nm despite the narrow range of
pH readings obtained. A likewise narrow range of tenderometry readings resulted in no
useful correlation with the spectra.
Overall the spatial multiplexed imaging with a DMA based light modulation is successful.
The theoretical analysis of multiplexing gives a general description of the system
performance, particularly for multiplexing with the Hadamard matrices. Experiments
show that the Hadamard multiplexing technique improves the SNR of spectra taken over
pointwise imaging. Aspects of the theoretical analysis are demonstrated. Hyperspectral
images are acquired and analysed that demonstrate that the spectra acquired are sensible
and useful.

year: 2009

title: Is there long-run convergence among regional house prices in the UK?

authors: Holmes, Mark J.

subjects: house price

abstract: This paper investigates the long-run convergence of regional house prices in the UK. Existing studies have failed to reach a consensus on whether or not regional house prices exhibit long-run convergence with each other. The application is proposed of a new test involving unit root testing of the first principal component based on regional—national house price differentials. Using mix-adjusted quarterly data for 1973—2006, it is found that the first principal component is stationary. This suggests that all UK regional house prices are driven by a single common stochastic trend. Further analysis suggests that those regions that are more distant from London exhibit the highest degrees of persistence with respect to deviations in house price differentials.

text: Is there long-run convergence among regional house prices in the UK? This paper investigates the long-run convergence of regional house prices in the UK. Existing studies have failed to reach a consensus on whether or not regional house prices exhibit long-run convergence with each other. The application is proposed of a new test involving unit root testing of the first principal component based on regional—national house price differentials. Using mix-adjusted quarterly data for 1973—2006, it is found that the first principal component is stationary. This suggests that all UK regional house prices are driven by a single common stochastic trend. Further analysis suggests that those regions that are more distant from London exhibit the highest degrees of persistence with respect to deviations in house price differentials.

year: 2008

title: He Matapihi Mā Mua, Mō Muri: The Ethics, Processes, and Procedures Associated with the Digitization of Indigenous Knowledge—The Pei Jones Collection

authors: Whaanga, Hēmi

abstract: The digital era has transformed how people live their lives and interact with the world and knowledge systems around them. In Aotearoa/New Zealand a range of initiatives incorporating Indigenous knowledge have been implemented to collect, catalog, maintain, and organize digital objects. In this article, we report on the ethics, processes, and procedures associated with the digitization of the manuscripts, works, and collected taonga (treasures) of the late Dr. Pei Te Hurinui Jones—and describe how it was transformed into a digital library. It discusses the decision-making processes and the various roles and responsibilities of the researchers, family members, and institute in this process.

text: He Matapihi Mā Mua, Mō Muri: The Ethics, Processes, and Procedures Associated with the Digitization of Indigenous Knowledge—The Pei Jones Collection The digital era has transformed how people live their lives and interact with the world and knowledge systems around them. In Aotearoa/New Zealand a range of initiatives incorporating Indigenous knowledge have been implemented to collect, catalog, maintain, and organize digital objects. In this article, we report on the ethics, processes, and procedures associated with the digitization of the manuscripts, works, and collected taonga (treasures) of the late Dr. Pei Te Hurinui Jones—and describe how it was transformed into a digital library. It discusses the decision-making processes and the various roles and responsibilities of the researchers, family members, and institute in this process.

year: 2015