# US 2013/0156340 A1 · Image Filtering by Sparse Reconstruction on Affinity Net

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- Number: US 2013/0156340 A1
- Document ID: US20130156340A1
- Status: Published application
- Kind: A1
- Application number: 13/330,795
- Filed: 2011-12-20
- Published: 2013-06-20
- Earliest claimed: 2011-12-20
- Assignees: Mitsubishi Electric Research Laboratories, Inc.
- Inventors: Fatih Porikli; Rajagopalan Sundaresan
- Web page: https://patentgrep.com/patent/US20130156340A1

## CPC

- G06T 5/70: Denoising; Smoothing
- G06T 2207/10044: Radar image
- G06T 2207/20072: Graph-based image processing
- G06T 2207/20076: Probabilistic image processing
- G06T 2207/20081: Training; Learning
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

A method reduces multiplicative and additive noise in image pixels by clustering similar patches of the pixels into clusters. The clusters form nodes in an affinity net of nodes and vertices. From each cluster, a dictionary is learned by a sparse combination of corresponding atoms in the dictionaries. The patches are aggregated collaboratively using the dictionaries to construct a denoised image.

## Claims

### Claim 1

A method for reducing multiplicative and additive noise in an image including pixels, comprising the steps of:
clustering similar patches of the pixels in the image into clusters, wherein the dusters form nodes in an affinity net of nodes and vertices;
learning, from each cluster, a dictionary by a sparse combination of corresponding atoms in the dictionaries, wherein the dictionary is under-complete when a size of the dictionary is much smaller than a rank of the cluster matrix; and
aggregating collaboratively the patches using the dictionaries to construct a denoised image, wherein the steps are performed in a processor.

### Claim 2 (depends on 1)

The method of claim 1, wherein the image is a synthetic aperture radar (SAR) and a pattern of the noise pattern is speckle noise and artifact.

### Claim 3 (depends on 1)

The method of claim 1, wherein the learning: uses an alternative decision process applied to the affinity net.

### Claim 4 (depends on 1)

The method of claim 1, wherein the nodes correspond to the patches and the vertices correspond to similarity between the nodes.

### Claim 5 (depends on 1)

The method of claim 1, wherein each cluster is in a form of a cluster matrix, and further comprising:
decomposing each cluster into a linear function of the corresponding dictionary and sparse coding coefficients to learn the dictionary that best represents coherent variations in the cluster.

### Claim 6 (depends on 5)

The method of claim 5 wherein the learning further comprises:
determining a projection error for columns of the cluster matrix;
determining inter-coefficient convergence from the projection errors.
selecting sparse coefficients as a set that gives a minimum projection and divergence errors to update the dictionary; and
determining a residual as a termination criterion.

### Claim 7

(canceled)

### Claim 8 (depends on 1)

The method of claim 1, further comprising:
filtering each cluster by the corresponding dictionary.

### Claim 9 (depends on 1)

The method of claim 1, further comprising:
reconstructing the nodes by a orthogonal matching pursuit procedure.

### Claim 10 (depends on 1)

The method of claim 1, wherein single node can participate in different clusters.

### Claim 11 (depends on 1)

The method of claim 1, wherein some nodes are singular without vertices.

### Claim 12 (depends on 1)

The method of claim 1, wherein the affinity net is a weighted a weighted graph where weights ω correspond to similarities between the patches.

### Claim 13 (depends on 1)

The method of claim 1, wherein an affinity between patches pi and pj is determined as
ω

(
p
i
,
p
j
)
=
〈
p
i
,
p
j
〉
=
∑
k
=
1
K


p
i
,
k

p
j
,
k
,
(
2
)
where k is a index, and K is a size of the patch in pixels.

### Claim 14 (depends on 13)

The method of claim 13, further comprising:
retaining only patches where the weight w is greater than a threshold τ.

### Claim 15 (depends on 1)

The method of claim 1, wherein the dictionary has only two atoms.

### Claim 16 (depends on 1)

The method of claim 1, wherein the dictionary has one atom.

### Claim 17 (depends on 1)

The method of claim 1, further comprising:
applying a logarithm-transform to the image;
subtracting a nonzero mean of the noise from the logarithm-transformed image; and
taking an exponent of a final estimate to produce the denoised image.

### Claim 18 (depends on 6)

The method of claim 6, further comprising:
adding an inter-coefficient divergence term in an objective function to penalize for coefficient divergences.

### Claim 19 (depends on 18)

The method of claim 18, wherein the dictionary D and sparse coefficients X are determined b optimizing an objective function
(
D
,
X
*
)
=
arg


min
D
,
X


λ


DX
-
C

2
2
+
μ

∑
i



x
i

0
+
∑
i



Dx
i
-
R
i

X

2
2
+
λ
2

∑
i


∑
j



x
i
-
x
j

2
,
where argmin return a minimal value, λ is a scalar to regulate a fidelity an a reconstruction to the image, μ is a scalar to adjust an amount of a imposed sparseness in the reconstruction, C represents the cluster matrix, Ri is a patch index operator, and λ2 is a scalar to regulate a divergence between sparse coefficients.

### Claim 20 (depends on 5)

The method of claim 5, wherein the cluster patches are arranged as columns of the cluster matrix.