Reducing signal-dependent noise in digital cameras

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:
• SN
• _
• ⁡
• (
• x
• ,
• y
• )
• =
• (
• I
• INR
• ⁡
• (
• x
• ,
• y
• )
• (
• I
• INR
• ⁡
• (
• x
• ,
• y
• )
• )
• 2
• +
• γ
• λ
• )
• ⁢
• I
• _
• ⁡
• (
• x
• ,
• y
• )
• 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), IINR(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.

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)I0(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 I0(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.

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)I0(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 I0(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.