Reducing signal-dependent noise in digital cameras

1. A method for producing a noise-reduced digital image captured using a digital imaging system having signal-dependent noise characteristics, comprising using a digital processor to perform at least some of the steps of:

a) capturing one or more noisy digital images of a scene, wherein said at least one noisy digital image has signal-dependent noise characteristics;

b) defining a functional relationship to relate the one or more noisy digital images to a noise-reduced digital image estimate, wherein the functional relationship includes at least two sets of unknown parameters, and wherein at least one of the sets of unknown parameters relates to the signal-dependent noise characteristics, wherein the functional relationship is:

I ( x,y )= β ( x,y ) I 0 ( x,y )+ η ( x,y )

where I (x,y) is a vector of pixels from the one or more noisy digital images at pixel location (x,y), β (x,y) and η (x,y) are function parameter vectors at pixel location (x,y), and I 0 (x,y) is the noise-reduced digital image estimate at pixel location (x,y), and wherein β (x,y) relates to the signal-dependent noise characteristics;

c) defining an energy function responsive to the functional relationship which includes at least:

i) a data fidelity term to enforce similarities between the one or more noisy digital images and the noise-reduced digital image estimate; and

ii) a spatial fidelity term to encourage sharp edges in the noise-reduced digital image estimate; and

d) using an optimization process to determine a noise-reduced image responsive to the energy function.

2. The method of claim 1 wherein β (x,y) has the form:

β ( x,y )= 1 +K 1 η ( x,y )

where K 1 is a parameter relating to the amplitude of the signal dependent noise, and 1 is a vector containing all 1s.

3. The method of claim 1 wherein the data fidelity term is defined by

( β ( x,y ) I 0 ( x,y )− I ( x,y ) t ( β ( x,y ) I 0 ( x,y )− I ( x,y ))

where ( ) t denotes a transpose operation.

4. The method of claim 1 wherein the spatial fidelity term is defined by

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where | V I 0 (x,y)| is the absolute value of the gradient of the noise-reduced digital image estimate at pixel location (x,y).

5. The method of claim 1 wherein the energy function g(I 0 (x,y), β (x,y), λ, α, γ) is defined by:

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where λ, α and γ are weighting parameters.

6. The method of claim 5 wherein the optimization of the energy function includes utilizing an alternating minimization algorithm on g(I 0 , β , λ, α, γ).

7. The method of claim 6 wherein the alternating minimization algorithm includes a steepest descent optimization.

8. The method of claim 1 further including the step of spatially registering the captured noisy digital images prior to determining the noise-reduced image.

9. The method of claim 8 wherein the step of spatially registering the captured noisy digital images includes selecting one captured noisy digital image as a reference digital image and applying translation, rotation or scaling operations to the other captured noisy digital images to align them with the reference digital image.

10. The method of claim 9 wherein the translation, rotation or scaling operations are applied to subsets of the image pixels in the other captured noisy digital images when only portions of the captured noisy digital images are misaligned.

11. The method of claim 1 wherein the one or more digital images are captured using a digital camera.

12. A method for producing a noise-reduced digital image captured using a digital imaging system having signal-dependent noise characteristics, comprising using a digital processor to perform at least some of the steps of:

a) capturing a plurality of digital images of a scene;

b) computing a noise-reduced image by combining the plurality of captured digital images;

c) determining estimates of scaled noise images for the plurality of digital images responsive to the captured digital images and the noise reduced image using the following equation:

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where I (x,y) is a vector of pixels from the one or more noisy digital images at pixel location (x,y), SN (x,y) is the vector of the pixel values of the scaled noise images at pixel location (x,y), I INR (x,y) is the value of the intermediate noise-reduced image at pixel location (x,y) and λ, are γ weighting parameters;

d) computing an updated noise-reduced image responsive to the previous noise-reduced image, the captured digital images, and the estimated scaled noise images;

e) computing updated estimates of the scaled noise images responsive to the captured digital images and the updated noise reduced image; and

f) repeating steps d) and e) until a convergence criterion is satisfied.

13. The method of claim 12 wherein the step of combining the plurality of captured digital images includes averaging the plurality of captured digital images.

14. The method of claim 12 wherein the updated noise-reduced image is calculated using the following equation:

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where I NR (x,y) and I INR (x,y) are pixel values of noise-reduced image and intermediate noise-reduced image, respectively, at pixel location (x,y), τ, and α are weighting parameters, “●” represents the dot product, “|•|” is the absolute value operator, and V is the gradient operator.

15. The method of claim 12 wherein the convergence criteria is based on performing a predefined number of iterations.

16. The method of claim 12 wherein the convergence criteria is based on a mean squared difference between noise-reduced images for two successive iterations.

17. The method of claim 16 wherein the convergence criteria further includes a predefined maximum number of iterations.

18. A method for producing a noise-reduced digital image captured using a digital imaging system having signal-dependent noise characteristics, comprising using a digital processor to perform at lest some of the steps of:

a) capturing one or more noisy digital images of a scene, wherein said at least one noisy digital image has signal-dependent noise characteristics;

b) defining a functional relationship to relate the one or more noisy digital images to a noise-reduced digital image estimate, wherein the functional relationship includes at least two sets of unknown parameters, and wherein at least one of the sets of unknown parameters relates to the signal-dependent noise characteristics, wherein the functional relationship is:

I ( x,y )= β ( x,y ) I 0 ( x,y )+ η ( x,y )

where I (x,y) is a vector of pixels from the one or more noisy digital images at pixel location (x,y), β (x,y) and η (x,y) are function parameter vectors at pixel location (x,y), and I 0 (x,y) is the noise-reduced digital image estimate at pixel location (x,y), and wherein β (x,y) relates to the signal-dependent noise characteristics;

c) defining an energy function responsive to the functional relationship which includes at least:

i) a data fidelity term to enforce similarities between the one or more noisy digital images and the noise-reduced digital image estimate; and

ii) a spatial penalty term to encourage sharp edges in the noise-reduced digital image estimate; and

d) determining a noise-reduced image by evaluating the energy function to select between candidate noise-reduced images.

19. A system comprising:

a data processing system; and

a memory system communicatively connected to the data processing system and storing instructions configured to cause the data processing system to implement a method for producing a noise-reduced digital image captured using a digital imaging system having signal-dependent noise characteristics, wherein the instructions comprise:

a) capturing one or more noisy digital images of a scene, wherein said at least one noisy digital image has signal-dependent noise characteristics;

b) defining a functional relationship to relate the one or more noisy digital images to a noise-reduced digital image estimate, wherein the functional relationship includes at least two sets of unknown parameters, and wherein at least one of the sets of unknown parameters relates to the signal-dependent noise characteristics, wherein the functional relationship is:

I ( x,y )= β ( x,y ) I 0 ( x,y )+ η ( x,y )

where I (x,y) is a vector of pixels from the one or more noisy digital images at pixel location (x,y), β (x,y) and η (x,y) are function parameter vectors at pixel location (x,y), and I 0 (x,y) is the noise-reduced digital image estimate at pixel location (x,y), and wherein β (x,y) relates to the signal-dependent noise characteristics;

c) defining an energy function responsive to the functional relationship which includes at least:

i) a data fidelity term to enforce similarities between the one or more noisy digital images and the noise-reduced digital image estimate; and

ii) a spatial fidelity term to encourage sharp edges in the noise-reduced digital image estimate; and

d) using an optimization process to determine a noise-reduced image responsive to the energy function.