Signal Processing - November 2017 - 10

Open problems in medical imaging
Medical image reconstruction is the pro-
cess of forming interpretable images from
the data recorded by an imaging system.
Until recently, there have been two pri-
mary methods for image reconstruction:
analytical and iterative. Analytical meth-
ods use idealized mathematical models
for the imaging system. Typically, these
techniques consider only the geometry
and sampling properties of the imaging
system and ignore details of the system
physics and measurement noise. These
reconstruction approaches have been
used extensively because they require
modest computation.
Over the past two decades, image re-
construction has evolved from the exclu-
sive use of analytical methods to a wider
use of model-based approaches that ac-
count for the physics and statistics. Usu-
ally the problems are ill posed, so that
maximum-likelihood (ML) methods
would propagate excessive noise from
the measurements into the reconstruct-
ed image. Using priors or regularizers
can overcome this limitation. A popular
approach is to base iterative methods
on maximum a posteriori (MAP) esti-
mation. MAP estimation encompasses
1) modeling the system, 2) developing
signal models to serve as priors, 3) de-
veloping faster optimization algorithms,
and 4) assessing the quality of the re-
constructed image.
The transition from analytical to it-
erative algorithms took place at widely
different dates in different modalities.
In positron emission tomography (PET)
and single-photon emission computed
tomography (SPECT), a seminal paper
on an expectation maximization (EM)
algorithm in the early 1980s led to more
than a decade of research before a key ac-
celeration method called ordered subsets
(OS) (related to incremental gradients in
the optimization field) helped lead to the
commercial adoption of OS-EM for clin-
ical PET and SPECT in about 1997, using
an (unregularized) ML approach. This
transition provided a dramatic improve-
ment in image quality. Human PET scan-
ners only recently began to provide MAP
methods clinically using a modification
of a Gaussian Markov random field prior
and a convergent OS algorithm.
10

In X-ray computed tomography
(CT), iterative image reconstruction first
became available commercially for the
CT part of SPECT-CT scanners in about
2010, using a different OS algorithm
published a decade earlier. In 2012, the
first U.S. Food and Drug Administration
(FDA)-approved iterative MAP method
targeted at reduced X-ray dose became
available for clinical CT, building on an
IEEE Transactions on Signal Processing paper from two decades earlier. This
approach also uses a modified Gaussian
MRF to make it edge preserving.
In MRI, researchers studied iterative
techniques to quantify relaxation param-
eters, reconstruct data from multiple re-
ceive coils, and correct for magnetic field
inhomogeneities. A turning point was
the introduction of compressed sensing
in about 2005, spawning an explosion of
research that finally led to FDA approval
of compressed sensing MRI products in
2017 using combinations of total variation
regularization and wavelet sparsifying
transforms. In all of the aforementioned
examples, more than a decade passed be-
tween the key publication and commercial
availability of the method!
Commercial MAP techniques use rela-
tive simple priors defined mathematically.
The emerging research trend is to explore
signal models that are learned from data.
In X-ray CT, there are numerous images
acquired at "normal" X-ray doses from
which one can learn signal models to use
later for reconstructing images from lowdose data. Another data-driven option
is to learn a sparse signal model during
image reconstruction, rather than relying
on training data, called blind or adaptive
dictionary (or transform) learning. This
data-driven evolution provides opportu-
nities for signal processing researchers to
explore signal models that better solve in-
verse problems, particularly from limited
or noisy data.
One can "unroll the loop" of an itera-
tive reconstruction algorithm and treat it
as a sequence of processing steps akin to a
deep neural network and then use data to
train more aspects of the processing chain.
Recent conferences have seen an explo-
sion of such methods. There are many
significant challenges because such algo-
rithms are arguably even more nonlinear
IEEE SIGNAL PROCESSING MAGAZINE

|

November 2017

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(and opaque) than the edge-preserving
regularization techniques used clinically
today. Can one characterize the "resolu-
tion" and "noise" properties of such algo-
rithms? What is the best training metric:
MSE or diagnostic image quality? What if
a patient has significantly different image
features than those found in the training
data? How well will a method trained for
one system configuration (e.g., a certain
set of coils in MRI or a certain set of an-
gular views and pitch in CT) generalize to
other configurations? Some experts have
conjectured that "machine learning will
transform radiology significantly within
the next five years" but others point out
there are significant technical and legal
challenges. These questions and more
should provide numerous research op-
portunities for signal processors inter-
ested in inverse problems like medical
imaging [11].

Open problems in
graph signal processing
Today's data is being generated at
an unprecedented rate from a diversity
of sources. Examples include profile
information in social networks, stimuli
in brain connectivity networks, and traf-
fic flow in city street networks, among
others. A decade ago, a typical data set
was supported on a regular lattice; today,
the story is quite different. Data is sup-
ported on complex and irregular struc-
tures. Often, these structures are modeled
by graphs, as they are able to describe
both the structure and the data associ-
ated with that structure. For example,
in an online social network, a user's
profile may contain the user's date of
birth, school attended, professional or-
ganizations, and more. Each of these
attributes can form a subnetwork with
different properties. Using graphs, we
want to analyze data supported on such
complex structures, allowing us to mine
information from online social networks,
transportation networks, the power grid,
and more, in the same context. While
these are representatives of physicalworld graphs, other graphs may include
abstract concept networks such as knowl-
edge graphs and correlation graphs.
Data science on graphs has been
considered from several angles by graph



Table of Contents for the Digital Edition of Signal Processing - November 2017

Signal Processing - November 2017 - Cover1
Signal Processing - November 2017 - Cover2
Signal Processing - November 2017 - 1
Signal Processing - November 2017 - 2
Signal Processing - November 2017 - 3
Signal Processing - November 2017 - 4
Signal Processing - November 2017 - 5
Signal Processing - November 2017 - 6
Signal Processing - November 2017 - 7
Signal Processing - November 2017 - 8
Signal Processing - November 2017 - 9
Signal Processing - November 2017 - 10
Signal Processing - November 2017 - 11
Signal Processing - November 2017 - 12
Signal Processing - November 2017 - 13
Signal Processing - November 2017 - 14
Signal Processing - November 2017 - 15
Signal Processing - November 2017 - 16
Signal Processing - November 2017 - 17
Signal Processing - November 2017 - 18
Signal Processing - November 2017 - 19
Signal Processing - November 2017 - 20
Signal Processing - November 2017 - 21
Signal Processing - November 2017 - 22
Signal Processing - November 2017 - 23
Signal Processing - November 2017 - 24
Signal Processing - November 2017 - 25
Signal Processing - November 2017 - 26
Signal Processing - November 2017 - 27
Signal Processing - November 2017 - 28
Signal Processing - November 2017 - 29
Signal Processing - November 2017 - 30
Signal Processing - November 2017 - 31
Signal Processing - November 2017 - 32
Signal Processing - November 2017 - 33
Signal Processing - November 2017 - 34
Signal Processing - November 2017 - 35
Signal Processing - November 2017 - 36
Signal Processing - November 2017 - 37
Signal Processing - November 2017 - 38
Signal Processing - November 2017 - 39
Signal Processing - November 2017 - 40
Signal Processing - November 2017 - 41
Signal Processing - November 2017 - 42
Signal Processing - November 2017 - 43
Signal Processing - November 2017 - 44
Signal Processing - November 2017 - 45
Signal Processing - November 2017 - 46
Signal Processing - November 2017 - 47
Signal Processing - November 2017 - 48
Signal Processing - November 2017 - 49
Signal Processing - November 2017 - 50
Signal Processing - November 2017 - 51
Signal Processing - November 2017 - 52
Signal Processing - November 2017 - 53
Signal Processing - November 2017 - 54
Signal Processing - November 2017 - 55
Signal Processing - November 2017 - 56
Signal Processing - November 2017 - 57
Signal Processing - November 2017 - 58
Signal Processing - November 2017 - 59
Signal Processing - November 2017 - 60
Signal Processing - November 2017 - 61
Signal Processing - November 2017 - 62
Signal Processing - November 2017 - 63
Signal Processing - November 2017 - 64
Signal Processing - November 2017 - 65
Signal Processing - November 2017 - 66
Signal Processing - November 2017 - 67
Signal Processing - November 2017 - 68
Signal Processing - November 2017 - 69
Signal Processing - November 2017 - 70
Signal Processing - November 2017 - 71
Signal Processing - November 2017 - 72
Signal Processing - November 2017 - 73
Signal Processing - November 2017 - 74
Signal Processing - November 2017 - 75
Signal Processing - November 2017 - 76
Signal Processing - November 2017 - 77
Signal Processing - November 2017 - 78
Signal Processing - November 2017 - 79
Signal Processing - November 2017 - 80
Signal Processing - November 2017 - 81
Signal Processing - November 2017 - 82
Signal Processing - November 2017 - 83
Signal Processing - November 2017 - 84
Signal Processing - November 2017 - 85
Signal Processing - November 2017 - 86
Signal Processing - November 2017 - 87
Signal Processing - November 2017 - 88
Signal Processing - November 2017 - 89
Signal Processing - November 2017 - 90
Signal Processing - November 2017 - 91
Signal Processing - November 2017 - 92
Signal Processing - November 2017 - 93
Signal Processing - November 2017 - 94
Signal Processing - November 2017 - 95
Signal Processing - November 2017 - 96
Signal Processing - November 2017 - 97
Signal Processing - November 2017 - 98
Signal Processing - November 2017 - 99
Signal Processing - November 2017 - 100
Signal Processing - November 2017 - 101
Signal Processing - November 2017 - 102
Signal Processing - November 2017 - 103
Signal Processing - November 2017 - 104
Signal Processing - November 2017 - 105
Signal Processing - November 2017 - 106
Signal Processing - November 2017 - 107
Signal Processing - November 2017 - 108
Signal Processing - November 2017 - 109
Signal Processing - November 2017 - 110
Signal Processing - November 2017 - 111
Signal Processing - November 2017 - 112
Signal Processing - November 2017 - 113
Signal Processing - November 2017 - 114
Signal Processing - November 2017 - 115
Signal Processing - November 2017 - 116
Signal Processing - November 2017 - 117
Signal Processing - November 2017 - 118
Signal Processing - November 2017 - 119
Signal Processing - November 2017 - 120
Signal Processing - November 2017 - 121
Signal Processing - November 2017 - 122
Signal Processing - November 2017 - 123
Signal Processing - November 2017 - 124
Signal Processing - November 2017 - 125
Signal Processing - November 2017 - 126
Signal Processing - November 2017 - 127
Signal Processing - November 2017 - 128
Signal Processing - November 2017 - 129
Signal Processing - November 2017 - 130
Signal Processing - November 2017 - 131
Signal Processing - November 2017 - 132
Signal Processing - November 2017 - 133
Signal Processing - November 2017 - 134
Signal Processing - November 2017 - 135
Signal Processing - November 2017 - 136
Signal Processing - November 2017 - 137
Signal Processing - November 2017 - 138
Signal Processing - November 2017 - 139
Signal Processing - November 2017 - 140
Signal Processing - November 2017 - 141
Signal Processing - November 2017 - 142
Signal Processing - November 2017 - 143
Signal Processing - November 2017 - 144
Signal Processing - November 2017 - 145
Signal Processing - November 2017 - 146
Signal Processing - November 2017 - 147
Signal Processing - November 2017 - 148
Signal Processing - November 2017 - 149
Signal Processing - November 2017 - 150
Signal Processing - November 2017 - 151
Signal Processing - November 2017 - 152
Signal Processing - November 2017 - 153
Signal Processing - November 2017 - 154
Signal Processing - November 2017 - 155
Signal Processing - November 2017 - 156
Signal Processing - November 2017 - 157
Signal Processing - November 2017 - 158
Signal Processing - November 2017 - 159
Signal Processing - November 2017 - 160
Signal Processing - November 2017 - 161
Signal Processing - November 2017 - 162
Signal Processing - November 2017 - 163
Signal Processing - November 2017 - 164
Signal Processing - November 2017 - 165
Signal Processing - November 2017 - 166
Signal Processing - November 2017 - 167
Signal Processing - November 2017 - 168
Signal Processing - November 2017 - 169
Signal Processing - November 2017 - 170
Signal Processing - November 2017 - 171
Signal Processing - November 2017 - 172
Signal Processing - November 2017 - 173
Signal Processing - November 2017 - 174
Signal Processing - November 2017 - 175
Signal Processing - November 2017 - 176
Signal Processing - November 2017 - Cover3
Signal Processing - November 2017 - Cover4
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