Local methods
The design of efficient despeckling filters is a
long-standing problem that has been the object of intense research
since the advent of SAR technology. The most straightforward way to
reduce these fluctuations and estimate the values of the physical
parameters is to average several independent samples from the data. This
operation, called multilooking, was applied in various forms from the
very beginning of the SAR era. However, such averaging that applies
equally to every region of the image, regardless of the local
heterogeneity, strongly degrades the spatial resolution.
In the
beginning of 2000s, Lee et al. proposed to use adaptive filtering for
polarimetric and interferometric SAR denoising. Instead of estimating
the parameters over a rectangular sliding window, a directional window
is locally selected among eight edge-aligned windows according to the
local gradient of the amplitude images. Lee’s method preserves the edge
structures since values of pixels on each side of the edge are never
combined together, avoiding the smoothing effects. Unfortunately, this
method tends to leave a high variance in homogeneous areas and create
some undesired artifacts.
The intensity-driven
adaptive-neighborhood (IDAN) technique was proposed for the polarimetric
and interferometric SAR parameter estimation. Following the idea of
filtering over directional windows, the IDAN performs a complex
multilooking operation on an adaptive neighborhood. This adaptive
neighborhood is constructed with a region-growing algorithm where the
most similar adjacent pixels are selected iteratively according to their
intensity values. The adaptive neighborhood aims to select as many
pixels as possible, all following the same statistical population as the
considered pixel. This decreases the resolution loss in the estimation
since noisy values coming from other populations are rejected. Due to
its window-shaped adaptivity, the IDAN achieves the best trade-off
between the residual noise and resolution loss among window-based
methods. However, due to its connectivity constraint, the IDAN leaves a
high variance in regions where there are only few adjacent similar
pixels.
The following generation of filtering approaches
introduced stronger priors to guide the solution. The first family
includes the variational-based methods which have gradually been
utilized for SAR image despeckling. Those methods are stable and
flexible and break through the traditional idea of filters by solving
the problem of energy optimization. Although these methods have achieved
good reduction of speckle noise, the result is usually dependent on the
choice of the model parameters and prior information, and is often
time-consuming. In addition, the variational-based methods cannot
accurately describe the distribution of speckle noise, which also
constraints the performance of speckle noise reduction.
The
second large family of approaches is based on wavelet transforms. Due to
their spatially localized and multiresolution basis functions, wavelets
yield sparse yet accurate representations of natural images in the
transform domain. Sharp discontinuities and pointlike features, so
common in SAR images, are well described by a small number of basis
functions, just like the large homogeneous regions between them. The
major weaknesses of this type of approach are the backscatter mean
preservation in homogeneous areas, details preservation, and producing
artificial effect into the results such as ring effects.
Non-local methods
The
non-local means (NLM) algorithm has provided a breakthrough in detail
preservation in SAR image despeckling. During the recent years, powerful
and widespread methods such as PPB, NL-SAR and SAR-BM3D have been
created. In the following paragraph, we will describe the essentials of
the algorithm. Figure 1 summarizes the processing steps.
Figure 1. Non-local estimation in action: processing at pixel x.
Non-local
estimation methods generally follow a three-step scheme with many
possible variations at each step and, possibly, preprocessing steps
and/or iterative refinement of results by repeated non-local
estimations. The first step identifies similar patches (patch size is
generally set from 3x3 to 11x11 pixels). It must reliably find, within
an extended search window (typically 21x21 to 39x39 pixels), patches
that are close to the reference central patch. Recurring patches are
found in smooth regions, but just as well around region boundaries,
textures, artificial structures, etc., as shown in figure 2. Once
several patches have been selected, they are assigned relative weights.
Figure
2. Fragments of SAR images: (a) homogeneous region, (b) line, (c)
texture, (d) structure. For each target patch (green) several similar
patches (red) are found in the same fragment [1].
The second step
combines patches, according to their weights, to form an estimate of
either the central pixel (pixel-wise estimation), the central patch
(patch-wise estimation), or all selected patches (stack-wise
estimation). The estimates computed from all possible reference patches
are then merged in a last step to produce the final image.
The
most straightforward way to combine patches is to use pixel-wise
filtering. Within this approach, a weight is assigned for the central
pixel of all the patches. By using those weights, the estimation for the
central pixel in a target patch is calculated.
The difference in
patch-wise filtering is that all pixels in the patch, not just the
central one, are estimated at once. Since each pixel is estimated
several times, a suitable aggregation phase is necessary to combine all
such estimates. The simplest form of aggregation is to consider uniform
weights for all the estimated pixels. Another strategy is to set the
weight associated with each estimate as inversely proportional to its
variance.
To illustrate why patch-wise estimation improves
performance, let us consider the special case of a pixel near the
boundary between two homogeneous regions. Since the patch centered on it
is strongly heterogeneous, most other patches of the search area,
coming from homogeneous regions on either side of the boundary, are
markedly dissimilar from it, and contribute very little to the average.
The estimate, thus, involves only a small effective number of
predictors, those along the edge, which results in a high variance. As a
result, a visible “halo” of residual noise is observed near the edges, a
phenomenon well-known in NLM, also referred to as the rare patch
effect. The target pixel, however, belongs to a large number of patches,
not just the patch centered on it, many of them drawn from the
homogeneous region to which the pixel belongs. In patch-wise
reprojection, all of these patches are included in the average reducing
the estimate variance, especially if suitable weights are used to take
into account the reliability of each contribution.
Let us now
consider the third strategy, with stack-wise filtering. The first
difference with regard to patch-wise filtering is that now all patches
collected in the stack are collaboratively filtered before reprojecting
them to their original position. The major improvement is that the stack
is filtered in three dimensions, i.e, not only along the stack but also
in the spatial domain. In SAR-BM3D, the whole stack, formed by just a
limited number of similar patches, is wavelet transformed, Wiener
filtered, and back transformed. By so doing, strong spatial structures
are emphasized through filtering while random noise is efficiently
suppressed. As a matter of fact, these techniques exhibit significant
improvements especially in highly structured areas (edges, point
reflectors, textures). The efficiency of collaborative filtering comes
from the full exploitation of the redundancy of information in a stack
of similar patches.
The performance of NLM methods depends on the
setting of several parameters, like patch size and search area size,
which should be related to image resolution, smoothing strength, and
balance between original and pre-estimated data. In most of the
non-local approaches these parameters are set by hand. Few works have
considered semisupervised setting or automatic setting with spatial
adaptation. NL-SAR is one of such publicly available methods that
automatically tunes patch and search window sizes and prefiltering
strengths to provide improved results.
Speckle filtering in KappaZeta
In
KappaZeta we analyzed, modified and combined multiple published methods
when designing a custom speckle filter for KappaOne service. For
details, take a look at our newsletter from April 2022.
[1]
https://doi.org/10.1109/MSP.2014.2311305