Highly accelerated imaging and image reconstruction using adaptive sparsifying transforms

Patent metadata

Field	Value
Publication number	US-9734601-B2
Application number	US-201514678876-A
Country	US
Kind code	B2
Filing date	Apr 3, 2015
Priority date	Apr 4, 2014
Publication date	Aug 15, 2017
Grant date	Aug 15, 2017

Abstract

A system executes efficient computational methods for high quality image reconstructions from a relatively small number of noisy (or degraded) sensor imaging measurements or scans. The system includes a processing device and instructions. The processing device executes the instructions to employ transform learning as a regularizer for solving inverse problems when reconstructing an image from the imaging measurements, the instructions executable to: adapt a transform model to a first set of image patches of a first set of images containing at least a first image, to model the first set of image patches as sparse in a transform domain while allowing deviation from perfect sparsity; reconstruct a second image by minimizing an optimization objective comprising a transform-based regularizer that employs the transform model, and a data fidelity term formed using the imaging measurements; and store the second image in the computer-readable medium, the second image displayable on a display device.

First claim

What is claimed is:

1. A system comprising:
at least one processing device;
non-transitory computer-readable medium storing instructions executable by the at least one processing device to employ transform learning as a regularizer for reconstructing an image from limited or corrupted imaging measurements, to generate a reconstructed image, wherein the limited or corrupted imaging measurements include a component that is a function of at least two pixels of the reconstructed image, wherein ones of the at least two pixels reside in different image patches of a plurality of image patches of the reconstructed image, and the instructions to cause the at least one processing device to:
reconstruct the image, from the imaging measurements, by iterative minimization of an adaptive image reconstruction optimization objective comprising a transform-model-based image regularizer and a data fidelity term formed using the limited or corrupted imaging measurements, wherein the minimization is expressed as

min
x

⁢

f
⁡

(

x
,
y

)

+

λ
⁢

⁢

J
⁡

(
x
)

⁢

(
i
)

,

wherein x is the reconstructed image, y are the imaging measurements, f (x, y) is the data fidelity term that includes interactions between data from the different image patches, λ is a regularization strength parameter, and J(x) is the transform-model-based image regularizer of the reconstructed image, which is obtained as an approximate minimum solution to a transform learning minimization problem that comprises:
sparsification error of the plurality of image patches of the reconstructed image, comprising a measure of discrepancy between the plurality of image patches transformed by a transform operator and sparse approximations of the plurality of image patches, wherein the sparse approximations comprise sparse codes; a sparsity promoting function that is one of a penalty or a set of constraints on the sparse approximations to the plurality of images patches; and a transform learning regularizer that controls properties of the transform operator; and
store the reconstructed image in the computer-readable medium, the reconstructed image displayable on a display device.

2. The system of claim 1 , wherein the plurality of image patches comprise a set of second image patches that approximate a plurality of reconstructed image patches of the reconstructed image.

3. The system of claim 2 , wherein the instructions are further executable by the at least one processing device to solve an adaptive image reconstruction optimization problem in conjunction with solving the transform learning minimization problem by performing minimization that alternates between solving for one or more of: (i) the transform operator; (ii) the sparse codes; (iii) the set of second image patches; and (iv) the reconstructed image in a signal domain.

4. The system of claim 2 , wherein J(x) is an approximation to a minimum solution, J opt (X), of the transform learning minimization problem expressed as one of:

J
opt

⁡

(
x
)

=

min

Φ
,
Z

⁢

∑

j
=
1

N
x

⁢

⁢

h
⁡

(

Φ
⁢

⁢

x
j

,

z
j

)

+

α
⁢

⁢

Q
⁡

(
Φ
)

+

γ
⁢

⁢

g
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(
Z
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;

(
ii
)

Assignees

• Univ Illinois

Inventors

• Bresler Yoram
• Pfister Luke A
• Ravishankar Saiprasad

Classifications

• G06T12/20 Primary

  Inverse problem, i.e. transformations from projection space into object space · CPC title

• G06T2211/424

  Iterative · CPC title

• G06T11/006 Primary

  Physics · mapped topic