WO2007001236A1

WO2007001236A1 - Wavelet shrinkage pre-filtering of mr images for brain tissue segmentation

Info

Publication number: WO2007001236A1
Application number: PCT/SG2005/000214
Authority: WO
Inventors: Zujun Hou
Original assignee: Agency For Science, Technology And Research
Priority date: 2005-06-28
Filing date: 2005-06-28
Publication date: 2007-01-04

Abstract

Brain tissue image data is pre-processed to remove the skull therefrom. An estimation is made of the noise level in the signal to determine if it is severely noisy. For those parts of the data that are not severely noisy, the tissue is segmented using FCM clustering. For those parts of the data that are severely noisy, the tissue is wavelet pre-filtered before the tissue image contained therein is segmented. The wavelet pre-filtering involves estimating a shrinkage parameter, wavelet transforming the data, coefficient shrinkage of the transformed data and inverse wavelet transforming of the reduced set of coefficients.

Description

Wavelet Shrinkage Pre-fϊltering of MR Images for Brain Tissue Segmentation

Field of the Invention

The present invention relates to noise reduction in magnetic resonance (MR) images, especially for brain tissue segmentation.

Background of the Invention

With the frequent application of magnetic resonance imaging to brain abnormality diagnosis, the automatic analysis of the acquired images using computer- aided diagnostic systems helps in the understanding of the development of lesions and assists in planning surgery, hi implementing such a computer-aided diagnostic system, an important consideration is brain tissue segmentation. A number of methods of segmenting brain tissue are known, which can roughly be classified as histogram-based or context-based.

Histogram-based methods cluster the data from histograms of the images, and include Gaussian modelling or fuzzy c-means (FCM) clustering. Gaussian modelling is exemplified by Z. Liang, J.R. MacFall and D.P. Harrington, in "Parameter estimation and tissue segmentation from multispectral images", IEEE Trans, of Medical Imaging 13, 1994, pp. 441-449. FCM clustering is exemplified by M.E. Brandt, T.P. Bohan, L.A. Kramer and J.M. Fletcher, in "Estimation of CSF, white and grey matter volumes in hydrocephalic children using fuzzy clustering of MR images", Comput. Medical Imaging & Graphics 18, 1994, pp. 25-34.

The main advantage of these methods is the low computation cost, which is important for real time applications. However, since only the intensity information is taken into account, the performance of these methods unavoidably suffers from perturbations, such as noise or intensity inhomogeneity.

To make the segmentation algorithm resistant to noise, spatial information from pixels/voxels, besides the intensity, can be considered. Systems that take this approach are classified as context-based segmentation methods. Basically, context-based methods constrain the solution with the image context, and yield a smoother segmentation map. Examples include random field modelling, as described by J.C. Rajapakse, J.N. Giedd and J.L. Rapoport, in "Statistical approach to segmentation of single-channel cerebral MR images", IEEE Trans, of Medical Imaging 16, 1997, pp. 176-186. Another method is regularized fuzzy c-means clustering, described by D. L. Pham, in "Spatial models for fuzzy clustering", Computer Vision and Image Understanding 84, 2001, pp. 285-297. This latter approach is a modification of histogram-based FCM clustering, with the purpose of the modification to make the algorithm more robust to noise.

Compared with histogram-based methods, context-based methods are more stable in the presence of noise, but much less efficient in implementation and computation cost.

Noise removal from MR image data is also known.

J. C. Wood and K. M. Johnson, in "Wavelet packet denoising of MR images: importance of Rician noise at low SNR", Magnetic Resonance in Medicine 41, 1999, pp. 631-635, proposed to denoise MR images using wavelet package transform. However, to apply the method to 3-D noise removal would be very demanding on computer memory. In addition, the computation of parameters needed, such as the threshold and noise level, is not cheap in computation costs.

R. D. Nowak, in "Wavelet-based Rician noise removal for MRI", IEEE Trans, on Image Processing, vol. 8 (10), 1999, pp. 1408-1419, also presented a method for MR image noise removal by wavelet transform. In particular, the method derived the necessary parameters based on the assumption that the noise distribution follows the Rician distribution. The method requires the discrete square wavelet transform as well as the usual discrete wavelet transform, thus increasing the requirements on computer memory. Furthermore, the threshold used is calculated voxel by voxel; hence the method is computationally expensive. There is a need for an approach to noise reduction in image signals which at least partially alleviates or avoids at least one or more of the disadvantages of at least some of the prior art.

Summary

According to one aspect of the present invention, there is provided a method of determining a threshold, t, for thresholding wavelet transformed image data for reducing noise in the image data, wherein t = σ{/σ_x, where

O_ξ denotes a standard deviation of a noise level S_n in the image data; σ_x denotes a standard deviation in the transformed image data; and r is a shrinkage parameter whose value is based on a noise level S_n in the image data.

According to a second aspect of the present invention, there is provided a threshold determined according to the method of the first apsect.

According to a third aspect of the present invention, there is provided a method of wavelet pre-filtering to reduce noise in image data, comprising: wavelet transforming the image data; thresholding the transformed image data using the threshold of the second aspect; and inverse transforming the thresholded transformed image data.

According to a fourth aspect of the present invention, there is provided a method of segmenting tissue in image data, comprising: wavelet pre-filtering the image data, according to the method of the third aspect; and segmenting tissue in the noise-reduced image data. According to a fifth aspect of the present invention, there is provided a method of segmenting tissue in MR image data, comprising: determining if the MR image data is noisy; reducing noise in the MR image data based on whether the image data is determined to be noisy; and segmenting tissue in the MR image data, including in the noise-reduced MR image data.

According to a sixth aspect of the present invention, there is provided a method of clinical diagnosis comprising reviewing a segmented image provided using the method of the fourth or fifth aspect.

A seventh aspect of the present invention provides treating a diagnosis made according to sixth aspect.

According to an eighth aspect of the present invention, there is provided apparatus for determining a threshold, t, for thresholding wavelet transformed image data for reducing noise in the image data, wherein

where ø_ξ denotes a standard deviation of a noise level S_n in the image data; σ_x denotes a standard deviation in the transformed image data; and r is a shrinkage parameter whose value is based on a noise level S_n in the image data.

This apparatus may be operable according to the method of the first aspect.

The present invention also provides apparatus for wavelet pre-filtering image data to reduce noise therein and apparatus for segmenting tissue in image data.

According to a ninth aspect of the present invention, there is provided a computer program product comprising computer readable program code for performing the method of any one of the first to sixth aspects. According to a preferred embodiment, brain tissue image data is pre-processed to remove the skull therefrom. An estimation is made of the noise level in the signal to determine if it is severely noisy. For those parts of the data that are not severely noisy, the tissue is segmented using FCM clustering. For those parts of the data that are severely noisy, the tissue is wavelet pre-filtered before the tissue image contained therein is segmented. The wavelet pre-filtering involves estimating a shrinkage parameter, wavelet transforming the data, coefficient shrinkage of the transformed data using the shrinkage parameter and inverse wavelet transforming of the reduced set of coefficients.

Introduction to the Drawings

The invention is described by way of non-limitative example, with reference to the accompanying drawings, in which:- Figure 1 is a flowchart of a method of image segmentation according to an embodiment of the invention;

Figure 2 is a schematic diagram of apparatus for performing image segmentation in image data;

Figures 3 A and 3B are axial brain scan images before and after pre-processing, respectively;

Figures 4A and 4B display surface rendering results of segmented grey matter and white matter, respectively;

Figure 5 is a flowchart of a method of pre-filtering image data according to an embodiment of the invention; Figure 6 is a schematic diagram of apparatus for performing image data pre- filtering;; and

Figure 7 is a schematic representation of a computer system suitable for performing the techniques described with reference to Figures 1, 2, 5 and 6.

Detailed Description

Figure 1 is a flowchart of a method of image segmentation according to an embodiment of the invention. Figure 2 is a schematic diagram of apparatus 10 for performing image segmentation, for example according to the method of the flowchart of Figure 1.

To develop a relatively stable and also relatively efficient method for tissue segmentation, the preferred embodiment pre-filters the image using wavelet shrinkage before histogram-based segmentation, hi particular, a method to estimate the noise level is used for determining the parameters of wavelet shrinkage.

The MR image data volume is input (step S 102), with the data representing images of sequential slices. The data may, for example, be provided straight from a scanner 12, from a memory 14 (e.g. a disc or computer memory), from a WAN or LAN or from some other source.

The MR image data volume is pre-processed (step S 104) by pre-processing means 16. The pre-processing, for example with MRI data of a brain, may be used to remove the skull/scalp for the image data, which is typically done through morphological operation and connected component analysis or atlas-guided active contours (for example, Sandor and Leahy, "Surface-based labelling of cortical anatomy using a deformable atlas", IEEE Trans. Medical Imaging 17 (1) 1990, 41-54). Other forms of pre-processing may include intensity in-homogeneity correction. Figure 3 A is an axial brain scan image before pre-processing, including the skull 30 and brain tissue 32. Figure 3B is an axial brain scan image after pre-processing, where the skull has been removed from the image, leaving only the brain tissue 32.

After this, the main brain tissue including white matter (WM), grey matter (GM) and cerebrospinal fluid (CSF) can be identified and will be subject to further processing as is described later.

A noise level S_n is determined for the pre-processed MR data (step S 106), once for the whole volume, in noise level estimating means 18. The noise level S_n is most usefully estimated from a relatively homogeneous region in the image domain, for example from the background, hi Tl -weighted brain MR images, a simple method to determine the background region is to use a threshold, Tb, to raster-scan the image. If the intensity of a pixel/voxel is less than T_b, then it is classified as the background pixel/voxel. The threshold can itself be estimated using existing methods, for example, the Otsu method. [For more detail, see Shan, Yue and Liu, "Automated histogram-based segmentation in Tl -weighted three-dementional magnetic resonance head images", Neurolmage 17, 2002, pp. 1587-1598, or Sijbers and Dekker, "Maximum likelihood estimation of signal amplitude and noise variance from MR data", Magnetic Resonance in Medicine 51, 2004, pp. 586-594]. It is found that estimating from the background is less affected by the intrinsic tissue variance than estimating from some specific tissue. Thus, in the preferred embodiment, the variance of the background is used to estimate S_n, S_n = ∑(x,. - x)² /(n_b - l) (1), where the summation is over all the background pixels/voxels, Xi is the intensity at position i, x is the mean value and n_b is the number of background pixels/voxels.

A determination is made of whether the noise level is severe (step S 108), for instance by comparing the noise level S_n with a threshold T_n, in comparator means 20. Through the study of phantom data, it has been found that for brain tissue segmentation a useful threshold level is T_n=4. This threshold is empirically estimated from phantom data where the noise level and the ground-truth are known. The use of a threshold T_n is advantageous as the process of noise removal could also blur the edge structure in the images. The threshold T_n provides a useful cut-off point in balancing the disadvantages of blurred edge structures against the advantages of de-noising.

If the noise level is determined in the comparator means 20 to be above the threshold, it is judged to be severe and the MR data is forwarded to a wavelet pre- filtering means 22 to be wavelet pre-filtered (step Sl 10). If the noise level is determined in the comparator means 20 to be below the threshold, it is judged not to be severe and the process continues on to for image segmentation (step Sl 12) in an image segmenting means 24. After wavelet pre-fϊltering (step Sl 10) in the wavelet pre-filtering means 22, the process also proceeds on to image segmentation (step Sl 12) in the image segmenting means 24. By the time the data reaches the image segmentation step (step Sl 12), it is either considered not to be noisy or else has been de-noised in the wavelet pre-filtering step (step Sl 10). Image segmentation (step Sl 12) can take various forms, particularly histogram based methods. In this embodiment the preferred approach classifies the de- noised tissue data using the FCM clustering method to segment the brain tissue into CSF, GM and WM. The FCM method is implemented in a grey-level histogram of the brain tissue, for instance as is described by M.E. Brandt et al., in "Estimation of CSF, white and grey matter volumes in hydrocephalic children using fuzzy clustering of MR images", mentioned earlier.

A segmentation map of the imaged tissue, such as brain tissue is output (step Sl 14).

In the method as described above, the skull removal occurs prior to the de- noising of the noisy portions, in step SIlO. In an alternative embodiment, the skull removal (if it is used at all), may occur after the de-noising but before segmentation.

Figures 4A and 4B display surface rendering results of GM 40 and WM 42, respectively, of a segmented map, using the preferred embodiment when applied to real data.

Figure 5 is a flowchart of a method of pre-filtering image data according to an embodiment of the invention, for instance as may be used in step S 110 of Figure 1. Figure 6 is a schematic diagram of apparatus 22 for performing pre-filtering, for example according to the method of the flowchart of Figure 5.

The image model widely used in MR image processing is: x = αx' + ξ, where x is the measured intensity, α the inhomogeneity field, x' the true intensity and ξ the noise.

The preferred approach to de-noising ignores the inhomogeneity field, and works quite reasonable when a < 20%.

Denoising using wavelets usually consists of the following steps: (1) wavelet transform of images; (2) thresholding the detail coefficients and (3) inverse wavelet transform.

One of two approaches to thresholding may typically be used, hard-thresholding, and soft-thresholding. If"*" is a threshold, the hard-thresholding function is defined as x x-l {\x\ > t} (2) and the soft-thresholding function is x sgnfø)-max(|x| - 1,0) (3) where x denotes a detail coefficient in the transform domain. Usually the soft- thresholding is advantageous over the hard one in terms of de-noising effect.

A state of the art de-noising method using wavelet transform is the BayesShrink method proposed by Chang, Yu and Vetterli, "Adaptive wavelet thresholding for image denoising and compression", IEEE Trans. Image Processing 9, 2000, pp. 1532-1546. The band-adaptive threshold is derived in a Bayesian framework and can be approximated by

σ . where σ_ξ and σ_x, denote the standard deviation of noise and the standard deviation of true image coefficients in a detail sub-band, respectively.

The BayesShrink method has been demonstrated to be very competitive with existing de-noising methods. However its performance is less effective when applied directly to MR images. The reason may be due to the Gaussian assumption on the noise distribution, which is not followed in MR images. It is known that the noise distribution in MR images is better described by the Rician distribution. Nevertheless, to avoid heavy computation and inspired by the BayesShrink method, the preferred method uses the assumption that the "optimal band-adaptive threshold" is still related to the strength of noise and signal in the following formula σ; t — ^■

where parameter r characterizes the strength of the shrinkage due to the thresholding. A large value of r will yield a large value oft, thus a large portion of detail coefficients would be suppressed. In contrast, a small r will lead to the preservation of most detail coefficients. For convenience, r is called the shrinkage parameter. In a detail sub-band, this embodiment computes the standard deviation of observed wavelet coefficients σ_x , rather than the standard deviation of true wavelet coefficients σ/υx the BayesShrink method. These two quantities are related by σ_x ²=σ_x ²S_n ².

In this embodiment of pre-filtering, the shrinkage parameter r is estimated (step

S 122) in a shrinkage parameter estimating means 52, for the pre-processed image data.

Parameter r is closely related to the noise level in a signal. In general, the more severe the noise level, the larger the value of r. Suppose that r = f(S_n). This function is approximated from tests on phantom data (for instance using a phantom generated as described by D.L. Collins, A.P. Zijdenbos, V. Kollokian, J.G. Sled and NJ. Kabani, in :Design and construction of a realistic digital brain phantom", IEEE Trans, on Medical Imaging 17, 1998, pp. 463-468.) by regression. The noise level and ground-truth are known with the phantom data. Thus, an "optimal" parameter r can be obtained numerically for each noise level. This provides a set of sample data for variables r and S_n, from which a curve between r and S_n can be fitted by methods such as the least square method.

Through experiment, it was determined that r could be reasonably estimated using a third order polynomial: r = aS_n ³ + bS_n ² + cS_n + d (4), where a, b, c and d are constants. Further experiment obtained the following empirical formula: r = 0.026S_n ³ - 0.518S_n ² + 3.524S_n - 5.994 to predict the shrinkage parameter r. Constants "c" and "d" can vary more than "a" and "b". For instance "c" can usefully be in the range of from 3.4 to 3.6; and "d" can usefully be in the range of from 5.9 to 6.1.

The standard deviation of noise and observed signal σ_ξ and σ_x are estimated as follows: σ, = A and

^σx ^~ VΣ^^X'' ^{~ X} tissue) / (ⁿ tissue ^~ I) > where the summation is over coefficients in a detail sub-band corresponding to tissue pixels/voxels as identified after the scalp removal process, * _ti_ssue represents the mean value, and ⁿ _ti_ssue represents the number of tissue coefficients in the above detail band. Here, the detail coefficients corresponding to tissue types are simply identified by a small threshold, £ = 10^~4. After the scalp removal, all non-tissue regions have been zeroed; thus coefficients contributed from these region in a detail sub-band will be zero. If the absolute value of a detail coefficient is greater than the small number, that coefficient can only result from tissue pixels/voxels.

The pre-processed image data undergoes wavelet transformation (step S 124), at a wavelet transforming means 54.

Wavelet transform is used here because of an inherent feature of wavelets: time- frequency localization. In this preferred embodiment, Mallat's algorithm is employed to compute the wavelet transform, for instance as described in Mallat, "A theory for multiresolution signal decomposition: the wavelet representation", IEEE Trans. Pattern Analysis and Machine Intelligence 11, 1989, pp. 674-693. The Mallat's algorithm filters the image by low-pass and high-pass filters, and each output is down-sampled by a factor of 2, after which the procedure is recursively repeated on the decimated low-pass band until the desired level of decomposition is reached. When the desired level is reached depends on the image resolution. For 256x256 images, 2~3 level suffices. For higher resolution such as 512x512, 4 level would yield more satisfactory results.

In a similar manner to the Fourier transform, the input data is padded with zeros to the next integer power of two if the data size is not an integer power of 2.

Once "t" is determined, the wavelet transformed data undergoes coefficient shrinkage (step S 126) at a coefficient shrinkage means 56. More particularly, the detail coefficients in the wavelet domain are thresholded and a shrunk (reduced) coefficient set is produced

The inverse wavelet transform is applied to the thresholded coefficients (step S 128) in a wavelet inverse transforming means, resulting in de-noised data. Which can then be segmented, for instance as in step Sl 12 of Figure 1 or in the image segmenting means 24 of Figure 2.

Segmented images, especially brain tissue images provided using an embodiment of the present invention can be applied to pre-process MR images for further clinical diagnosis.

The de-noising method that is provided is computationally fast. Compared with the method proposed by Nowak, mentioned earlier, the preferred embodiment is around a factor often times faster in CPU time and leads to more accurate segmentation, based on phantom data.

The above embodiment is specifically designed to use data from MR data. Data from other sources of data such as CT, ultrasound images, etc. can be used provided that the shrinkage parameter is estimated accordingly. Wavelet filtering is also preferred. Other transforms could be used but would generally be less effective.

The various components in Figures 2 and 6 are referred to as "means", and will usually be embodied in circuits, constructed in hardware to perform a single operation or several operations, or programmed using software modules to perform those one or more operations. Possible embodiments maybe made up of dedicated hardware alone, a combination of some dedicated hardware and some software programmed hardware and software programmed hardware alone. Embodiments also include a conventional or other computer programmed to perform the relevant tasks.

A module, and in particular the module's functionality, can be implemented in either hardware or software. In the software sense, a module is a process, program, or portion thereof, that usually performs a particular function or related functions. In the hardware sense, a module is a functional hardware unit designed for use with other components or modules. For example, a module may be implemented using discrete electronic components, or it can form a portion of an entire electronic circuit such as an Application Specific Integrated Circuit (ASIC). Numerous other possibilities exist.

Figure 7 is a schematic representation of a computer system 200 suitable for performing the techniques described with reference to Figures 1, 2, 5 and 6. A computer 202 is loaded with suitable software in a memory, which software can be used to perform steps in a process that implement the techniques described herein (e.g. the steps of Figures 1 and/or 5). MRI data can be input, and segmentation results obtained using such a computer system 200. This computer software executes under a suitable operating system installed on the computer system 200.

The computer software involves a set of programmed logic instructions that are able to be interpreted by a processor, such as a CPU, for instructing the computer system 200 to perform predetermined functions specified by those instructions. The computer software can be an expression recorded in any language, code or notation, comprising a set of instructions intended to cause a compatible information processing system to perform particular functions, either directly or after conversion to another language, code or notation.

The computer software is programmed by a computer program comprising statements in an appropriate computer language. The computer program is processed using a compiler into computer software that has a binary format suitable for execution by the operating system. The computer software is programmed in a manner that involves various software components, or code means, that perform particular steps in the process of the described techniques.

The components of the computer system 200 include: the computer 202, input and output devices such as a keyboard 204, a mouse 206 and an external memory device 208 (e.g. one or more of a floppy disc drive, a CD drive, a DVD drive and a flash memory drive) and a display 210, as well as network connexions for connecting to the Internet 212. The computer 202 includes: a processor 222, a first memory such as a ROM 224, a second memory such as a RAM 226, a network interface 228 for connecting to external networks, an input/output (I/O) interface 230 for connecting to the input and output devices, a video interface 232 for connecting to the display, a storage device such as a hard disc 234, and a bus 236.

The processor 222 executes the operating system and the computer software executing under the operating system. The random access memory (RAM) 226, the readonly memory (ROM) 224 and the hard disc 234 are used under direction of the processor

222.

The video interface 232 is connected to the display 210 and provides video signals for display on the display 210. User input, to operate the computer 202 is provided from the keyboard 204 and the mouse 206.

The internal storage device is exemplified here by a hard disc 234 but can include any other suitable non- volatile storage medium.

Each of the components of the computer 202 is connected to the bus 236 that includes data, address, and control buses, to allow these components to communicate with each other.

The computer system 200 can be connected to one or more other similar computers via the Internet, LANs or other networks. The computer software program may be provided as a computer program product. During normal use, the program may be stored on the hard disc 234. However, the computer software program may be provided recorded on a portable storage medium, e.g. a CD-ROM read by the external memory device 208. Alternatively, the computer software can be accessed directly from the network 212.

In either case, a user can interact with the computer system 200 using the keyboard 204 and the mouse 206 to operate the programmed computer software executing on the computer 202.

The computer system 200 is described for illustrative purposes: other configurations or types of computer systems can be equally well used to implement the described techniques. The foregoing is only an example of a particular type of computer system suitable for implementing the described techniques.

Claims

1. A method of determining a threshold, t, for thresholding wavelet transformed image data for reducing noise in the image data, wherein t = σ_ξ ^r/σ_x, where σ_ξ denotes a standard deviation of a noise level S_n in the image data; σ_x denotes a standard deviation in the transformed image data; and r is a shrinkage parameter whose value is based on a noise level S_n in the image data.

2. A method according to claim 1, wherein the noise level S_n is determined from a relatively homogenous region of the image domain.

3. A method according to claim 2, wherein the image data has background pixels/voxels and the relatively homogenous region of the image domain comprises the background of the image.

4. A method according to any one of the preceding claims, wherein the noise level S_n in the image data is determined by:

S_n = ∑(x , - X)² Kn₁₃ - I), where the summation is over all the pixels/voxels of a predetermined region in the image data for which the noise level is being determined; Xi is the intensity at position i; x is the mean value; and

H_b is the number of background pixels/voxels.

5. A method according to any one of the preceding claims, wherein the shrinkage parameter r is determined is determined from a third order polynomial: r = aSn³ + bS_n ² + cS_n + d, where "a", "b", "c" and "d" are constants.

6. A method according to claim 5, wherein "c" is in the range of from 3.4 to 3.6; and "d" is in the range of from 5.9 to 6.1

7. A method according to claim 5, wherein r = 0.026S_n ³ - 0.52S_n ² + 3.52S_n - 5.99.

8. A method according to any one of the preceding claims, wherein σ_ξ, the standard deviation of a noise level S_n is determined from: øξ = S_n.

9. A method according to any one of the preceding claims, wherein σ_x, the standard deviation in the transformed image data is determined from:

^σx = V∑fe ^{~ X} tissuef '(J* tissue ^~O > where the summation is over coefficients in a detail sub-band corresponding to pixels/voxels identified as image data of interest; Xj is the wavelet coefficient at position i; ^x _tis_sue represents the mean value; and ^_ti_ssue represents the number of coefficients in the detail band.

s

10. A method according to claim 9, wherein the image data comprises tissue image data; and the tissue is identified as image data of interest.

11. A method according to claim 10, wherein the summation is over coefficients in a detail sub-band corresponding to identified tissue pixels/voxels; and n_ti_ssue represents the number of tissue coefficients in the detail band.

12. A method according to any one of the preceding claims, wherein σ_x, the standard deviation in the transformed image data is determined from the standard deviation of coefficients in a detail sub-band corresponding to types of image data of interest in the wavelet transform domain.

13. A method according to any one of the preceding claims further comprising determining one or more of: σ_ξ, the standard deviation of a noise level S_n in the image data; σ_x, the standard deviation in the transformed image data; and r, the shrinkage parameter.

14. A threshold determined according to the method of any one of the preceding claims.

15. A method of wavelet pre-filtering to reduce noise in image data, comprising: wavelet transforming the image data; thresholding the transformed image data using the threshold as defined in claim 14; and inverse Ixansforming the thresholded transformed image data.

16. A method according to claim 15, further comprising determining said threshold according to the method of any one of claims 1 to 13.

17. A method according to claim 15 or 16, wherein thresholding the wavelet ^■ transformed image data comprises band-adaptively thresholding the coefficients.

18. A method according to any one of claims 15 to 17, wherein thresholding the coefficients comprises soft-thresholding the coefficients.

19. A method according to any one of claims 15 to 18, wherein wavelet transforming the image data is based on Mallat's algorithm.

20. A method according to claim 19, wherein wavelet transforming the image data is based on Mallat's algorithm with 2-level decomposition.

21. A method according to any one of claims 15 to 20, further comprising preprocessing the image data to remove unwanted material therefrom.

22. A method according to claim 21, wherein pre-processing the image data occurs before determining the parameter for wavelet shrinkage.

23. A method according to claim 21 or 22, wherein the unwanted material comprises bone.

24. A method according to any one of claims 21 to 23, wherein the unwanted material comprises a skull.

25. A method according to any one of claims 21 to 24, further comprising identifying tissue after removing unwanted material from the image data.

26. A method of segmenting tissue in image data, comprising: wavelet pre-filtering the image data, according to the method of any one of claims 15 to 25; and segmenting tissue in the noise-reduced image data.

27. A method according to claim 26, further comprising determining if the image data is noisy and only wavelet pre-filtering to reduce noise on image data determined to

' be noisy.

28. A method according to claim 27, wherein determining if image data is noisy comprises estimating the noise level of the image data.

29. A method according to claim 28,^" wherein estimating the noise level of the image domain comprises estimating the noise level S_n.

30. A method according to any one of claims 27 to 29 when dependent on at least claim 20, wherein the image data for which it is determined if the image data is noisy, is image data that has already been pre-processed to remove unwanted material therefrom.

31. A method according to any one of claims 26 to 30, wherein segmenting tissue comprises using fuzzy c-means clustering of the noise-reduced image data.

32. A method according to any one of the preceding claims, wherein the image data comprises MR image data.

33. A method according to any one of the preceding claims, wherein the image data comprises image data of brain tissue.

34. A method of segmenting tissue in MR image data, comprising: determining if the MR image data is noisy; reducing noise in the MR image data based on whether the image data is determined to be noisy; and segmenting tissue in the MR image data, including in the noise-reduced MR image data.

35. A method according to claim 34, wherein image data that is determined not to be noisy is not subject to said reducing noise step prior to the segmenting step.

36. A method of clinical diagnosis comprising reviewing a segmented image provided using the method of any one of claims 26 to 35.

37. Treating a diagnosis made according to the method of claim 36.

38. A method according to any one of claims 1 to 37, wherein r, the shrinkage parameter is not equal to 2.

39. Apparatus for determining a threshold, t, for thresholding wavelet transformed image data for reducing noise in the image data, wherein t = σ{/σ_x, where σξ denotes a standard deviation of a noise level S_n in the image data; σ_x denotes a standard deviation in the transformed image data; and r is a shrinkage parameter whose value is based on a noise level S_n in the image data.

40. Apparatus according to claim 39, further comprising: means for determining σς, the standard deviation of a noise level S_n in the image data; means for determining σ_x, the standard deviation in the transformed image data; and means for determining r, the shrinkage parameter.

41. Apparatus according to claim 39 or 40, operable according to the method of any one of claims 1 to 13.

42. Apparatus for wavelet pre-filtering image data to reduce noise therein, comprising: wavelet transformer means for wavelet transforming the image data; thresholding means for thresholding the wavelet transformed image data using a threshold determined according to the method of any one of claims 1 to 14; and wavelet inverse transforming means for inverse transforming the shrunk coefficients of the wavelet transformed image data.

43. Apparatus according to claim 42 further comprising apparatus for determining a threshold, t, as defined in any one of claims 39 to 41.

44. Apparatus according to claim 42 or 43, further comprising pre-processing means for removing unwanted material from the image data.

45. Apparatus according to any one of claims 42 to 44 operable according to the method of any one of claims 15 to 25.

46. Apparatus for segmenting tissue in image data, comprising: apparatus for wavelet pre-filtering image data according to any one of claims 42 to 45; and image segmenting means for segmenting tissue in pre-filtered image data from the apparatus for wavelet pre-fϊltering.

47. Apparatus according to claim 46, further comprising: noise level estimating means for determining the noise level of the image data; and comparator means for comparing the determined noise level with a threshold to determine if the data is noisy.

48. Apparatus according to claim 46 or 47 operable according to the method of any one of claims 26 to 31.

49. Apparatus for segmenting tissue tissue in image data, comprising: means for determining if the image data is noisy; means for reducing noise in the image data based on whether the image data is determined to be noisy; and means for segmenting tissue in the image data, including in the noise-reduced image data.

50. Apparatus according to claim 49 operable according to the method of claim 34 or 35.

51. Apparatus according to any one of claims 39 to 50 being a computer system.

52. Apparatus according to any one of claims 39 to 50 being a computer program product.

53. A computer program product comprising computer readable program code for performing the method of any one of claims 1 to 37.

54. A method of wavelet pre-filtering MR image data substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.

55. A method of segmenting tissue in MR image data substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.

56. A method of determining a threshold, t, substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.