Abstract
A method for deriving a blur kernel from a blurred image is provided herein. The method may include the following steps: obtaining a blurred image B, being a product of a blur kernel k applied to an original image I; calculating fθ(x)=Rd*Pθ(B)(x) for every angle θ, wherein R denotes an autocorrelation operator, Pθ denotes a projection operator of based on angle θ, and d denotes a one dimensional differentiation filter; estimating spectral power of the blur kernel based on a given support parameter; estimating the blur kernel k using a phase retrieval algorithm, based on the estimated spectral power of the blur kernel; updating the support parameters; and repeating the estimating of the spectral power, the estimating of the kernel and the updating of the support parameters in an iterative, to yield the blur kernel.
Claims

A method comprising:
obtaining a blurred image B, being a product of a blur kernel k applied to an original image I, wherein B and I are matrices representing pixel image arrays and k is a kernel of a matrix;
calculating f_{θ}(x)=R_{d*Pθ(B)}(x) for every angle θ, wherein R denotes an autocorrelation operator, P_{θ} denotes a projection operator of a two dimensional signal into one dimension based on angle θ, and d denotes a one dimensional differentiation filter applied to a product of the projection operator P_{θ} and the blurred image B;
setting support parameters s_{θ} to argmin_{x }f_{θ}(x);
estimating {circumflex over (k)}^{2 }denoting a spectral power of the blur kernel based on a given support parameter;
estimating the blur kernel k using a phase retrieval algorithm, based on the estimated spectral power of the blur kernel {circumflex over (k)}^{2};
updating the support parameters s_{θ} to argmax_{x }(R_{Pθ(k)}(x)>a·max(R_{Pθ(k)})), wherein a is constant number; and
repeating the estimating of the spectral power {circumflex over (k)}^{2}, the estimating of the kernel and the updating of the support parameters s_{θ} in an expectation maximization (EM) procedure, to yield the blur kernel k.
 The method according to claim 1, wherein the projection operator P_{θ} is achieved by integrating the two dimensional signal along a direction orthogonal to the angle θ.
 The method according to claim 1, wherein blur kernel k represents the blur operation which transforms I to B due to movements of a capturing device upon capturing the blurred image.
 The method according to claim 1, wherein I is a natural image captured by an image capturing device.
 The method according to claim 1, wherein the angles θ are selected so that each selected angle corresponds with a pixel of the pixel array.
 The method according to claim 1, further comprising using the retrieved blur kernel k to retrieve the original image.
 The method according to claim 1, wherein a is between 0 and 1.

A system comprising:
A computer memory configured to obtain a blurred image B, being a product of a blur kernel k applied to an original image I, wherein B and I are matrices representing pixel image arrays and k is a kernel of a matrix; and
a computer processor configured to:
(a) calculate f_{θ}(x)=R_{d*Pθ(B)}(x) for every angle θ, wherein R denotes an autocorrelation operator, P_{θ} denotes a projection operator of a two dimensional signal into one dimension based on angle θ, and d denotes a one dimensional differentiation filter applied to a product of the projection operator P_{θ} and the blurred image B;
(b) set support parameters s_{θ} to argmin_{x }f_{θ}(x);
(c) estimate {circumflex over (k)}^{2 }denoting a spectral power of the blur kernel based on a given support parameter;
(d) estimate the blur kernel k using a phase retrieval algorithm, based on the estimated spectral power of the blur kernel {circumflex over (k)}^{2};
(e) updating the support parameters s_{θ} to argmax_{x }(R_{Pθ(k)}(x)>a·max(R_{Pθ(k)})), wherein a is constant number; and
(f) repeat the estimating of the spectral power {circumflex over (k)}^{2}, the estimating of the kernel and the updating of the support parameters s_{θ} in an expectation maximization (EM) procedure, to yield the blur kernel k.
 The system according to claim 8, wherein the projection operator P_{θ} is achieved by integrating the two dimensional signal along a direction orthogonal to the angle θ.
 The system according to claim 8, wherein blur kernel k represents the blur operation which transforms I to B due to movements of a capturing device upon capturing the blurred image.
 The system according to claim 8, wherein I is a natural image captured by an image capturing device.
 The system according to claim 8, wherein the angles θ are selected so that each selected angle corresponds with a pixel of the pixel array.
 The system according to claim 8, further comprising using the retrieved blur kernel k to retrieve the original image.
 The system according to claim 8, wherein a is between 0 and 1.

A computer program product comprising:
a nontransitory computer readable storage medium having computer readable program embodied therewith, the computer readable program comprising:
computer readable program configured to obtain a blurred image B, being a product of a blur kernel k applied to an original image I, wherein B and I are matrices representing pixel image arrays and k is a kernel of a matrix;
computer readable program configured to calculate f_{θ}(x)=R_{d*Pθ(B)}(x) for every angle θ, wherein R denotes an autocorrelation operator, P_{θ} denotes a projection operator of a two dimensional signal into one dimension based on angle θ, and d denotes a one dimensional differentiation filter applied to a product of the projection operator P_{θ} and the blurred image B;
computer readable program configured to set support parameters s_{θ} to argmin_{x }f_{θ}(x);
computer readable program configured to estimate {circumflex over (k)}^{2 }denoting a spectral power of the blur kernel based on a given support parameter;
computer readable program configured to estimate the blur kernel k using a phase retrieval algorithm, based on the estimated spectral power of the blur kernel {circumflex over (k)}^{2};
computer readable program configured to updating the support parameters s_{θ} to argmax_{x }(R_{Pθ(k)}(x)>a·max(R_{Pθ(k)})), wherein a is constant number; and
computer readable program configured to repeat the estimating of the spectral power {circumflex over (k)}^{2}, the estimating of the kernel and the updating of the support parameters s_{θ} in an expectation maximization (EM) procedure, to yield the blur kernel k.
 The computer program product according to claim 15, wherein the projection operator P_{θ} is achieved by integrating the two dimensional signal along a direction orthogonal to the angle θ.
 The computer program product according to claim 15, wherein blur kernel k represents the blur operation which transforms I to B due to movements of a capturing device upon capturing the blurred image.
 The computer program product according to claim 15, wherein I is a natural image captured by an image capturing device.
 The computer program product according to claim 15, wherein the angles θ are selected so that each selected angle corresponds with a pixel of the pixel array.
 The computer program product according to claim 15, further comprising computer readable program configured to use the retrieved blur kernel k to retrieve the original image.
Owners (US)

Jolly Seven Series 70 Of Allied Security Trust I
(Jun 06 2019)
Explore more patents:

Stepping Stone Series 85 Of Allied Security Trust I
(Oct 08 2018)
Explore more patents:
 Yissum Research Development Company Of The Hebrew University Of Jerusalem Ltd (Aug 13 2013)
Applicants

Yissum Res Dev Co
Explore more patents:
Inventors

Fattal Raanan
Explore more patents:

Goldstein Amit
Explore more patents:
IPC Classifications
US Classifications

382/255
Explore more patents:
Document Preview
 Publication: Apr 14, 2015

Application:
Jun 25, 2013
US 201313926756 A

Priority:
Jun 25, 2013
US 201313926756 A

Priority:
Jun 25, 2012
US 201261663747 P