3.1. Model Reconstruction Based on Sparse Bayesian Algorithm
In the design of garden landscape spatial environment, images often have complex structures
and diverse features, so traditional reconstruction methods cannot handle these complex
situations well. Sparse Bayesian algorithm is a machine learning technique used for
statistical inference, which has strong adaptability and high generalization ability,
and is therefore widely used in image reconstruction tasks. Sparse representation
theory is a multi-scale extended theoretical system that utilizes sparse constraints
and control signals to achieve signal decomposition. It has advantages such as high
efficiency and robustness in signal and data processing. Therefore, this theory has
been widely applied in fields such as feature extraction, noise suppression, and sparse
reconstruction [16]. The sparse Bayesian reconstruction algorithm in the IVR model can achieve the optimal
sparse representation of image feature information. And based on this, a lower dimensional
mathematical model can be established to solve practical application problems, thereby
achieving full mining and utilization of image information [17]. The structure of the multi-scale fusion module is shown in Fig. 1.
Fig. 1. Structure diagram of multi-scale fusion module.
According to Fig. 1, in sparse representation theory, all signals and data with sparse representation
space have compressibility. That is, both data and signals have a certain degree of
sparsity within a certain transformation domain [18]. Therefore, compress the decoder layers with scales of d0, d2, and d4 to their initial
sizes. Then, the compressed feature maps to their initial size are used as inputs
to the multi-scale fusion module through deconvolution layers. Finally, edge information
from different depths was fused separately. Based on this theory, if the unknown signal
is set to $x$ and the observation matrix is $\gamma $, then Eq. (1) is the mathematical expression of the signal observation equation.
In Eq. (1), the value range of unknown signal $x$ is $x\in H^{N} $. The range of values for
the observation matrix $\gamma $ is $\gamma \in H^{M\times N} $ where $N\ge M$. The
range of values for the measurement value $y$ of the observation matrix is $y\in H^{M}
$. $M$ and $N$ represent the columns and rows of the observation matrix, respectively.
The signal observation equation can restore complete data information from incomplete
data. However, in general, most raw data has insufficient sparsity. Therefore, it
is not possible to directly use Eq. (1) for reconstruction processing. Therefore, before reconstruction, it is necessary
to perform sparse decomposition on the original data through a transformation strategy.
Eq. (2) is a mathematical expression for sparse decomposition.
In Eq. (2), $\varphi _{i} $ means the sparse transformation matrix, i. e. the transformation
domain. $E$ is sparsity, where the range of values for transformation domain and sparsity
is $H^{N} $. Using the equivalent dictionary matrix $D=\varphi \gamma $, Eq. (3) is a mathematical expression for sparse reconstruction.
In Eq. (3), $D$ means the equivalent dictionary matrix. $\left\| \cdot \right\| _{0} $ is the
norm of vector $l_{0} $, which represents the number of non zero elements in the vector.
Taking into account factors such as noise and error during actual measurement, the
expression for sparse reconstruction can also be shown by Eq. (4).
In Eq. (4), $q$ represents the noise in actual measurement, and $\left\| E\right\| _{1} =\sum
{}_{i} \left|E_{i} \right| $ is the sum of absolute values of signal elements. Considering
practical applications, there is almost no situation without noise. Therefore, in
the presence of noise, the basic linear model expression for sparse reconstruction
is shown in Eq. (5).
In Eq. (5), $E_{i} $ means that the vector atom to be solved, i.e. the reconstructed signal
source result. $y\in H^{M\times 1} $ is known observation information, while $q\in
H^{M\times 1} $ means unknown observation noise, which is the noise vector in the
actual environment. $D\in H^{M\times N} $ is an underdetermined equivalent dictionary
matrix. Bayesian algorithm's core idea is to parameterize the prior information of
unknown vectors through Gaussian distribution. Furthermore, Bayesian theory was used
to update and alternate the implicit parameters of the posterior information of unknown
vectors. Thus, the final posterior distribution estimation was obtained [19]. The observation image was set as $y$. If the mean $q$ of the ambient noise is 0
and obeys the Gaussian distribution, then Eq. (6) is the Gaussian likelihood function of the observed image $y$.
In Eq. (6), $p$ represents the observation point, $\theta $ represents the parameter of the
Gaussian distribution, if the environmental noise is $q\sim N\left(0,\varepsilon ^{2}
\right)$ and $\theta =\varepsilon ^{-2} $, and according to Bayesian theory, $E$ in
the model follows a Gaussian distribution, then Eq. (7) is the prior distribution function.
In Eq. (7), $\Omega $ represents the implicit parameter controlling prior variance, with a value
range of $\Omega \buildrel\Delta\over= diag(\omega _{1}$, $\omega _{2}$, ..., $\omega
_{n})$. When $\omega _{i} $ is 0, the corresponding $E_{i} $ is also 0. Therefore,
Fig. 2 shows a sparse Bayesian reconstruction model.
According to Fig. 2, sparse Bayesian reconstruction model's central idea is to parameterize unknown vectors'
prior information by using Gaussian distribution. Therefore, this model can also be
seen as a multi task linear regression model of sparse Bayesian [20]. Therefore, to cope with more complex design of garden landscape spatial environment,
while considering more complex and diverse practical application scenarios, a multi-layer
prior reconstruction model is constructed based on sparse Bayesian reconstruction
model. Fig. 3 shows the IVR multi-layer prior model. This model essentially utilizes deeper hidden
parameters to further express the reconstructed model's conjugate distribution. The
accuracy parameter $\omega $ of IVR is controlled by the shape parameter $a$ and the
scale parameter $b$, respectively. The accuracy parameter $\theta $ of noise model
is controlled by shape parameter $g$ and scale parameter $f$, respectively, which
control the noise.
Fig. 2. Sparse bayesian reconstruction model diagram.
Fig. 3. Multilayer prior model graph for image visual reconstruction.
3.2. Optimized IVR Model Based on Landscape Spatial Environment Design
To construct an IVR model for garden landscape spatial environment design, sparsity
reconstruction can be performed on the image features of garden landscape spatial
environment design. And feature matching method can be used to detect the features
of garden landscape spatial environment design images. Atanassov extension method
can be used to match the feature points of garden landscape spatial environment design.
Fig. 4 shows the IVR model for garden landscape spatial environment design.
Fig. 4. Visual reconstruction model of landscape space environment design image in
landscape architecture.
According to Fig. 4, seed point $P$ means that landscape spatial environment design image's pixel set
is $\left(i,j\right)$. And $P$ is also spatial environment's pixel center. The reconstruction
model is composed of sharpened templates and blocks, where the grayscale value of
the pixel center is represented by $G_{swk} $. The subbands number is set to $K$.
Eq. (8) is the expression for the reconstructed model's gradient feature components.
In Eq. (8), $a$ is a motion blur feature vector. $b$ represents the number of columns in the
vector quantization matrix. This image reconstruction model combines fuzzy pixel region
feature fusion reconstruction method. From this, the pixel set of spatial environmental
artistic features distribution in garden landscapes was obtained. This has improved
garden landscapes' spatial environment design ability, as well as the three-dimensional
perception ability and image information reconstruction ability of spatial environment
design images. When constructing IVR models for landscape spatial environment design,
visual feature space distributed detection methods, image gray pixel feature separation
methods, and visual image multi-level feature decomposition methods are commonly used
[21]. An image visual feature reconstruction model for garden landscape spatial environment
design was constructed, where Eq. (9) is the calculation of the visual feature distribution of the image.
In Eq. (9), $Z\left(\vec{x}\right)$ represents the visual feature distribution of the image,
$p$ represents the pixel center of the seed point, $j$ represents the points in the
pixel set, and $Z_{j} \left(\vec{x}\right)$ represents the visual feature distribution
of point $j$ in the pixel set. The adaptive fusion method is used to reconstruct the
edge visual model of the garden landscape design, thereby obtaining the fuzzy closeness
function of the spatial environment image in Eq. (10).
In Eq. (10), $fitness\left(\vec{x}\right)$ represents the spatial environment image blur closeness
function, while $\alpha $ and $\beta $ represent the similarity and difference degrees
of blur closeness, respectively. From Eq. (10), it can be set that the coordinate of garden landscape spatial environment design
point $P_{N} $ is $\left(X_{PN} ,Y_{PN} \right)$. The coordinate of spatial environment
design edge point $L$ is $\left(x_{k} ,y_{k} \right)$. Eq. (11) represents the relationship between the coordinates of the design point $P_{N} $
and the edge point $L$.
The relationship between spatial design points in Eq. (11) can determine the grayscale pixel level $f$ of landscape spatial environment design.
Eq. (12) is the visual feature reconstruction model for the spatial environment of garden
landscapes.
In Eq. (12), $b_{a} =\left(\frac{1}{af_{\max } } -\frac{T}{2} \right)\left(1-a\right)$, where
$Ei\left(\cdot \right)$ is visual information feature recombination output in garden
landscape spatial environment design. The recombination result obtained by combining
model recognition can be used for garden landscape spatial environment design. To
improve environmental design capabilities, visual optimization of spatial environment
in garden landscape design can be carried out on this model. Fig. 5 shows the optimized IVR model for garden landscape spatial environment design.
Fig. 5. Optimized image visual reconstruction model diagram.
According to Fig. 5, after extracting the edge point $L$ of the spatial model, the local variance of
the visual image of the spatial environment was set to $\zeta _{1}^{2} $. The optimal
image coefficient for landscape spatial environment design is $\zeta _{\eta }^{2}
$. The value range of parameter $\beta $ is $\max \left[\frac{\zeta _{1}^{2} -\zeta
_{\eta }^{2} }{\zeta _{1}^{2} } ,~0\right]$. In IVR, the gradient descent method is
used for block wise visual reconstruction during visual region segmentation, so that
the designed image sparsity feature values meet $C\in Z$. The optimal visual reconstruction
threshold for designed image $f_{n} \left(x,y\right)$ at frame $n$ can be obtained.
At this point, garden landscape spatial environment design's image matching coefficient
is shown in Eq. (13).
In Eq. (13), $Q$ means a standardized constant. Distributed detection of the spatial environment
design of gardens was carried out by using block based template matching method. At
the same time, contour point matching method was used to extract edge features in
gardens spatial environment design. The maximum visual grayscale value of the obtained
garden landscape spatial environment design image is shown in Eq. (14).
In Eq. (14), the super-resolution reconstruction method and sparse representation method are
used to visually reconstruct the image of the garden landscape spatial environment
design. And the interactive genetic algorithm is combined to achieve landscape information
fusion perception in the garden landscape spatial environment design. The visual information
reconstruction model of the environmental design image obtained at this time is shown
in Eq. (15).
In Eq. (15), $p\left(x,y\right)$ refers to IVR model's grayscale image, $g\left(x,y\right)$ is
reconstructed vision image, and $f\left(x,y\right)$ represents garden landscape space's
initial environmental image.