Image de-noising method

Abstract

A multi-scale detail representation of an image is computed as a weighted sum of translation difference images. A denoising operator is applied to the translation difference images so that translation differences are modified as a function of an estimated local signal-to-noise ratio and at least one denoised center difference image at a specific scale is computed by combining denoised translation difference images at scale s or a finer scale. A denoised image is computed by applying a reconstruction algorithm to the denoised center difference images.

Claims

1. A method of denoising an image represented by a digital signal representation, the method comprising the steps of: creating at least one approximation image at at least one scale by applying a multi-scale decomposition algorithm to the image wherein all details of the at least one approximation image at a scale representing grey values of pixels of the image have been omitted; creating translation difference images by pixel-wise subtracting values of the at least one approximation image at a scale s and values of a translated version of the at least one approximation image; applying a denoising operator to translation difference values of the translation difference images so that the translation difference values are modified as a function of an estimated local signal-to-noise ratio to provide denoised translation difference images; computing at least one denoised center difference image at a specific scale by combining the denoised translation difference images at scale s or a finer scale; and computing a denoised image by applying a reconstruction algorithm which reverses the multi-scale decomposition algorithm to the at least one denoised center difference image; wherein the estimated local signal-to-noise ratio is estimated by comparing a translation difference to a selection of translation differences in a local neighborhood of the translation difference.

2. The method according to claim 1, wherein the selection of translation differences is defined as the translation differences having an orientation approximately perpendicular to an orientation of a translation difference of interest.

3. The method according to claim 2, further comprising the step of comparing the translation differences to a weighted average of the selection of translation differences in the local neighborhood.

4. The method according to claim 3, wherein weights of the weighted average are a function of a pair-wise distance between neighboring pixels and a central pixel and/or pair-wise differences between an orientation of neighboring translation differences and the orientation of the translation difference of interest.

5. The method according to claim 3, wherein the denoising operator applies a multiplicative correction factor to the translation differences.

6. The method according to claim 4, wherein the multiplicative correction factor is a function of a ratio of a magnitude of the translation difference and a magnitude of the weighted average of the selection of translation differences in the local neighborhood.

7. The method according to claim 1, wherein the image is a radiographic image.

8. A non-transitory computer readable medium comprising computer executable code adapted to carry out the steps of the method of claim 1 when executed on a computer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates how a center difference image at scale k is computed out of the approximation image at scale k-m.

(2) FIG. 2 illustrates a method of the present invention for noise correction making use of translation differences derived from approximation images at the same or finer scale.

(3) FIG. 3 shows a local neighbourhood around a pixel. The translation difference of interest is indicated by the pixel pair with bold border and the corresponding selection of translation differences T involved in the noise correction operator are indicated by the dashed borders.

(4) FIG. 4 is a legenda.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(5) The multi-scale image processing based on the translation difference images that are combined to center differences creates the possibility to reduce the noise present in the digital image.

(6) It is applicable to a reversible multi-scale detail representation that can be computed as a weighted sum of translation difference images.

(7) The weighing factors and the translation offsets of the translation difference images can be deducted from the multi-scale decomposition in such a way that the resulting weighted sum of the translation difference images is identical to or an approximation of the detail pixel values.

(8) To compute the weighted sum of translation difference images, the approximation image at the same scale (or resolution level) or the approximation images at the smaller scales (or finer resolution levels) can be used.

(9) For these multi-scale detail representations the noise can be reduced by applying a noise correction operator to the translation difference images before the weighted sum is computed.

(10) The pixel value at position i,j in the detail image d.sub.k can be computed out of an approximation image g.sub.l at the same or finer scale lε{0, . . . , k}.:

(11) $\begin{array}{c}{d}_k\left(i,j\right)=c_k\left(i,j\right)\\ =\underset{m}{\overset{}{.Math.}}\underset{n}{\overset{}{.Math.}}{w}_{m,n}\left(g_l\left(\mathrm{ri},\mathrm{rj}\right)-g_l\left(\mathrm{ri}+m,\mathrm{rj}+n\right)\right)\end{array}$

(12) The term g.sub.l(ri,rj)−g.sub.l(ri+m,rj+n) is called a translation difference.

(13) It expresses the difference in pixel value between a central pixel and a neighbouring pixel in an approximation image. It is a measure of local signal variation.

(14) The weighted sum of the translation differences is called a centre difference c.sub.k(i,j).

(15) In a first preferred embodiment for each pixel position i,j in the detail image the weights w.sub.m,n are computed such that the weighted sum of the translation differences matches exactly the pixel values in the detail image.

(16) In a second preferred embodiment the strict criteria for the weights w.sub.m,n is not enforced.

(17) The center difference c′.sub.k(i,j), which is in this preferred embodiment computed as weighted sum of a selection of translation differences, is an approximation of the corresponding pixel value in the detail image d.sub.k(i,j). By using a reduced selection of translation differences, a trade-off is generated between the speed and the quality of the multi-scale denoising.

(18) After denoising, each center difference c″.sub.k(i,j) is preferably corrected by applying a multiplicative correction factor d.sub.k(i,j)/c′.sub.k(i,j).

(19) The local pixel differences reflected in the translation differences g.sub.l(ri,rj)−g.sub.l(ri+m,rj+n) can be due to both noise and signal variations.

(20) To reduce the noise, translation differences are individually compared to other translation differences in a local neighbourhood.

(21) The local neighbourhood is defined by the extent of the selection of translation differences used to compute the center difference c.sub.k(i,j).

(22) According to a preferred embodiment of the method of the present invention, a translation difference is compared to the weighted average ave.sub.T of a selection of translation differences T in a local neighbourhood.

(23) Translation differences with a magnitude larger than the magnitude of the average ave.sub.T of a selection of translation differences T in a local neighbourhood indicate strong signal variation and needs to be preserved.

(24) Translation differences with a magnitude smaller than the magnitude of the average ave.sub.T indicate small noisy signal variations and can be reduced.

(25) By choosing an appropriate correction operator, noise reduction can be achieved while preserving the fine detail structures in the image.

(26) As a translation difference is defined as the difference between a central pixel and a neighbouring pixel in an approximation image, these 2 pixels define an orientation P.

(27) In one preferred embodiment of the present invention, the selection of translation differences T is defined as the translation differences with an orientation Q approximately perpendicular to orientation P.

(28) The weights to compute the weighted average ave.sub.T of the selection of translation differences T are defined as function of the pair-wise distance between the neighbouring pixels and the central pixel and (or) of the pair-wise differences between the 2 directions Q and P.

(29) In a preferred embodiment the ave.sub.T is computed as:

(30) ${\mathrm{ave}}_T=\underset{\left(m,n\right)\in T}{\overset{}{.Math.}}{\left(g_l\left(\mathrm{ri},\mathrm{rj}\right)-g_l\left(\mathrm{ri}+m,\mathrm{rj}+n\right)\right)}^{*}{A}^{*}{\sin \left(Q-P\right)}^{*}\mathrm{Exp}\left(\frac{-\left(m^2+n^2\right)}{B}\right)$
with A and B normalization constants.

(31) The noise reduction can then be achieved by applying a multiplicative correction factor per translation difference. The correction factor is defined as function of the ratio of the magnitude of the translation difference and the magnitude of the average ave.sub.T of the selection of translation differences T.

(32) In a preferred embodiment this function is:

(33) $\mathrm{noise\_corr}\mathrm{\_fact}\left(m,n\right)=\frac{.Math.g_l\left(\mathrm{ri},\mathrm{rj}\right)-g_l\left(\mathrm{ri}+m,\mathrm{rj}+n\right).Math.}{{b_k}^{*}.Math.{\mathrm{ave}}_T.Math.}-1$
with the multiplicative correction factor clipped between [0.0, 1.0].

(34) Factor b.sub.k specifies the amount of noise reduction per scale.

(35) The denoised centre differences are computed as the sum of the noise reduced translation difference images:

(36) $c_k\left(i,j\right)=\underset{m}{\overset{}{.Math.}}\underset{n}{\overset{}{.Math.}}{{w_{m,n}}^{*}\left(g_l\left(\mathrm{ri},\mathrm{rj}\right)-g_l\left(\mathrm{ri}+m,\mathrm{rj}+n\right)\right)}^{*}\mathrm{noise\_corr}\mathrm{\_fact}\left(m,n\right)$

(37) Finally the denoised version of the image is computed by applying the multi-scale reconstruction to the denoised centre difference images, i.e. the addition of the interpolated denoised centre difference images to obtain the full-resolution image.

(38) Having described in detail preferred embodiments of the current invention, it will now be apparent to those skilled in the art that numerous modifications can be made therein without departing from the scope of the invention as defined in the appending claims.