Signal Processing - September 2016 - 103
In this article, we measure the quality of a sensing matrix
as its spectral sensing coherence information with sparse
domain bases: . m ^U, W h def < I - W T U T UW< F , where I is the
identity matrix. Minimization of . m ^ U, W h imposes the condition that the Gram matrix W T U T UW be as close as possible to the identity matrix, which provides a good sensing
matrix as well.
Evaluation of undersampling systems
For the four types of undersampling systems, we examine
their sampling efficiency based on the spectral sensing coherence information of their sensing matrices, and then evaluate
their reconstruction accuracy on a diverse multispectral database containing images of various scenes-including indoor
scenes, outdoor scenes, various materials and different illuminations-from four online data sets [40]-[43]. A few example images are shown in Figure 7.
Computation of spectral sensing coherence information
and image reconstruction
The spectral sensing coherence information is computed
with respect to a domain basis in which the signals can be
420 nm
450 nm
480 nm
510 nm
540 nm
sparsely represented. From the multispectral image database, we learn two kinds of bases W in which multispectral
images have a sparse representation. The first is from principal components analysis (PCA) [45], which is applied to
derive an orthonormal bases. The second is from the K-SVD
algorithm [39], which is used to obtain an overcomplete dictionary. The bases represent the specific structural characteristics of the multispectral images and video frames, and
thus are suitable for computing spectral sensing coherence
information . m ^ U, W h and analyzing the sampling efficiency of the undersampling schemes for multispectral acquisition systems.
In computing the PCA bases and the overcomplete dictionary, we use 100,000 multispectral patches of size 10 # 10 # 29
pixels (horizontal # vertical # spectral) that are randomly
sampled from the database. The size of each basis element is
thus 10 # 10 # 29 as well. Since the PCA bases are orthonormal and complete, it has a size of exactly 2,900. For K-SVD,
6,200 atoms are learned as a sparse representation of the natural multispectral images.
We also synthetically test the reconstruction accuracy of
the four undersampling multispectral imaging systems on the
570 nm
600 nm
630 nm
660 nm
690 nm
Figure 7. Six example images from the multispectral database, including indoor and outdoor scenes, various materials, and different illumination. Ten of
the 29 spectral channels (from 420 nm to 700 nm, at 10 nm intervals) are shown. The corresponding RGB images are displayed in the top row.
IEEE SIgnal ProcESSIng MagazInE
|
September 2016
|
103
Table of Contents for the Digital Edition of Signal Processing - September 2016
Signal Processing - September 2016 - Cover1
Signal Processing - September 2016 - Cover2
Signal Processing - September 2016 - 1
Signal Processing - September 2016 - 2
Signal Processing - September 2016 - 3
Signal Processing - September 2016 - 4
Signal Processing - September 2016 - 5
Signal Processing - September 2016 - 6
Signal Processing - September 2016 - 7
Signal Processing - September 2016 - 8
Signal Processing - September 2016 - 9
Signal Processing - September 2016 - 10
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Signal Processing - September 2016 - 101
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Signal Processing - September 2016 - 103
Signal Processing - September 2016 - 104
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Signal Processing - September 2016 - 106
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Signal Processing - September 2016 - 110
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Signal Processing - September 2016 - 125
Signal Processing - September 2016 - 126
Signal Processing - September 2016 - 127
Signal Processing - September 2016 - 128
Signal Processing - September 2016 - 129
Signal Processing - September 2016 - 130
Signal Processing - September 2016 - 131
Signal Processing - September 2016 - 132
Signal Processing - September 2016 - 133
Signal Processing - September 2016 - 134
Signal Processing - September 2016 - 135
Signal Processing - September 2016 - 136
Signal Processing - September 2016 - 137
Signal Processing - September 2016 - 138
Signal Processing - September 2016 - 139
Signal Processing - September 2016 - 140
Signal Processing - September 2016 - 141
Signal Processing - September 2016 - 142
Signal Processing - September 2016 - 143
Signal Processing - September 2016 - 144
Signal Processing - September 2016 - 145
Signal Processing - September 2016 - 146
Signal Processing - September 2016 - 147
Signal Processing - September 2016 - 148
Signal Processing - September 2016 - 149
Signal Processing - September 2016 - 150
Signal Processing - September 2016 - 151
Signal Processing - September 2016 - 152
Signal Processing - September 2016 - 153
Signal Processing - September 2016 - 154
Signal Processing - September 2016 - 155
Signal Processing - September 2016 - 156
Signal Processing - September 2016 - 157
Signal Processing - September 2016 - 158
Signal Processing - September 2016 - 159
Signal Processing - September 2016 - 160
Signal Processing - September 2016 - 161
Signal Processing - September 2016 - 162
Signal Processing - September 2016 - 163
Signal Processing - September 2016 - 164
Signal Processing - September 2016 - 165
Signal Processing - September 2016 - 166
Signal Processing - September 2016 - 167
Signal Processing - September 2016 - 168
Signal Processing - September 2016 - 169
Signal Processing - September 2016 - 170
Signal Processing - September 2016 - 171
Signal Processing - September 2016 - 172
Signal Processing - September 2016 - 173
Signal Processing - September 2016 - 174
Signal Processing - September 2016 - 175
Signal Processing - September 2016 - 176
Signal Processing - September 2016 - Cover3
Signal Processing - September 2016 - Cover4
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