多尺度自适应稀疏表示提升高光谱图像分类性能
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本文主要探讨了"光谱-空间多尺度自适应稀疏表示(Spectral-Spatial Hyperspectral Image Classification via Multiscale Adaptive Sparse Representation, MASR)"在高光谱图像分类中的应用。高光谱成像（HSI）因其提供丰富的光谱信息而被广泛用于地球科学和遥感领域。传统的稀疏表示方法在HSI分类中表现出色，通过为每个测试像素定义一个局部区域，然后用一组共用的训练基（样本）联合表示区域内像素，从而利用了空间上下文信息。
然而，问题在于如何选择最适宜的区域尺度（大小），这对于不同结构类型的HSI来说是个挑战。不同的尺度可以捕捉到互补但相关的分类信息，这在传统方法中往往被忽视。因此，作者提出了一种多尺度自适应稀疏表示模型（MASR），其核心思想是利用多尺度的空间信息进行分类。MASR采用自适应稀疏策略，它不仅能够区分不同尺度区域内的像素特性，还能动态调整参数，以适应不同HSI数据集的复杂性和结构差异。
在MASR中，关键步骤包括：
1. **多尺度区域划分**：针对每个测试像素，根据图像的特性自适应地选择或组合多个不同尺度的邻域，以获取包含丰富信息的局部特征。
2. **自适应稀疏编码**：利用不同尺度下的训练样本，每个区域内的像素被编码为稀疏向量，这有助于提取最有代表性的特征，同时抑制噪声和冗余信息。
3. **稀疏度约束与优化**：通过引入自适应的稀疏性约束，模型能够在保持信息完整性的同时，减少非关键特征的影响，提高了分类的精度和效率。
4. **联合学习与融合**：结合来自不同尺度的稀疏表示结果，可能通过集成学习方法整合信息，以获得更准确的分类决策。
MASR的优势在于其灵活性和鲁棒性，它能根据不同HSI数据的特性动态调整处理策略，从而显著提升分类性能。这种方法对于处理复杂场景下的HSI分类任务具有重要的理论价值和实践意义，有望在遥感分析、环境监测和地理信息系统等领域得到广泛应用。
7740 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014
B. JSRM
In HSI, neighboring pixels that belong to the same material
usually are strongly correlated with each other. In [30], the
JSRM is introduced to capture such spatial correlations by
assuming that neighboring pixels within a region of fixed size
can be jointly represented by a few common atoms from a
structural dictionary. Specifically, the size of a region centered
at test pixel y
1
is denoted by W × W , and pixels within such
a region are denoted by {y
i
}
i=1,...,W ×W
. These pixels can also
be stacked into a matrix Y =[y
1
, y
2
,...,y
W ×W
], of the size
M × (W × W ). The matrix can be compactly represented as
Y =[y
1
, y
2
,...,y
W ×W
]=[Dα
1
, Dα
2
,...,Dα
W ×W
]
= D[α
1
, α
2
,...,α
W ×W
]=DA (8)
where A =[α
1
, α
2
,...,α
W ×W
] is the sparse coefficients
matrix corresponding to Y. Since the positions of nonzero
coefficients in [α
1
, α
2
,...,α
W ×W
] determine the indexes
of the selected atoms in D, the JSRM enables neighboring
pixels[y
1
, y
2
,...,y
W ×W
] to be represented by a small set of
common atoms, by enforcing a few nonzero rows on the sparse
coefficients matrix A. Then, matrix A can be obtained by
solving the following optimization problem:
ˆ
A =argmin
A
Y − DA
F
subject to A
row,0
≤ K (9)
where A
row,0
denotes the joint sparse norm, which is used
to select a number of the most representative nonzero rows in
A, and ·
F
is the Frobenius norm. A variant of the OMP
algorithm called the simultaneous OMP (SOMP) [34] can be
used to efficiently obtain an approximate solution. Note that,
enforcing the structured constraints (e.g., mixed L
1,2
[33] and
manifold [45]) on (9) may lead to a better sparse coefficients
matrix, but also create a higher computational cost. After
ˆ
A
is recovered, the label of test pixel y
1
can be decided by the
minimal total error, i.e.,
ˆc =argmin
c
Y − D
c
ˆ
A
c
F
,c=1,...,C (10)
where
ˆ
A
c
denotes the rows in
ˆ
A associated with the cth class.
By incorporating spatial information of local regions, the
JSRM can deliver much better classification results, in terms
of accuracy, compared to the pixelwise SRC model. However,
the region size (or, as we call it, the region scale) greatly affects
the classification performance. Fig. 1 shows the classification
results for the JSRM with varied region scales for three different
data sets. As can be observed in Fig. 1, different regions
favor different region scales. Specifically, detailed or near-edge
regions require a comparatively small region scale (e.g., ellipse
regions in Fig. 1) whereas large region scales are preferred for
smooth areas (e.g., rectangle regions in Fig. 1). Therefore, it is
not trivial to determine an optimal region scale for the JSRM.
III. P
ROPOSED MASR FOR HSI CLASSIFICATION
A. Multiscale Spatial Information in HSI
Given one test pixel y
1
in HSI, its T neighboring regions
are selected of different scales (sizes). Pixels within the se-
Fig. 1. Influence of region scales on the JSRM algorithm (Overall Accuracy
values are given in percentage). (a) Classification results obtained by the JSRM
algorithm on the Indian Pine image with region scales varying from 3 × 3to
15 × 15. (b) Classification results obtained by the JSRM algorithm on the Sali-
nas image with region scales varying from 3 × 3to15× 15. (c) Classification
results obtained by the JSRM algorithm on the University of Pavia image with
region scales varying from 3 × 3to15× 15.
lected regions can be arranged to construct the corresponding
multiscale matrix Y
multiscale
=[Y
1
,...,Y
t
,...,Y
T
], where
Y
t
includes pixels from the tth scale region. In HSI, regions
of different scales usually exhibit distinct spatial structures
and characteristics. Nonetheless, since all the different scales
correspond to the same test pixel y
1
, they should provide com-
plementary yet correlated information, which can be utilized to
classify y
1
more accurately.
B. Multiscale Spatial Information in HSI
Suppose that we have one structural dictionary D and the
multiscale matrix [Y
1
,...,Y
t
,...,Y
T
] for the test pixel y
1
.
Then, all the sparse representation problems of T scales (9) can
be rewritten together as
{
ˆ
A
t
}
T
t=1
=argmin
{A
t
}
T
t=1
Y
t
− DA
t
F
subject to A
t
row,0
≤ K ∀ 1 ≤ t ≤ T (11)
where [A
1
,...,A
t
,...,A
T
] are the sparse coefficients for
[Y
1
,...,Y
t
,...,Y
T
], which can constitute a multiscale
sparse coefficients matrix A
multiscale
. Such a problem can be
solved by separately applying the SOMP algorithm [34] on
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