WO2014197658A1

WO2014197658A1 - Method and system for noise standard deviation estimation

Info

Publication number: WO2014197658A1
Application number: PCT/US2014/041015
Authority: WO
Inventors: Ming Yan; Jiahua Fan; Meghan YUE
Original assignee: General Electric Company
Priority date: 2013-06-08
Filing date: 2014-06-05
Publication date: 2014-12-11
Also published as: CN104240184B; CN104240184A

Abstract

A noise standard deviation estimation method is provided. In the method, an input image containing noise is received and filtered to acquire a smoothed image. A noise map is generated as a difference between the input image and the smoothed image. After pre-removing edges in the noise map, a threshold T or a threshold function Tg is estimated from the edge pre-removed noise map. Then the threshold T or threshold function Tg is used to identify edges in the noise map and the identified edges are removed from the noise map to obtain an edge removed noise map. Noise standard deviation is estimated from the edge removed noise map.

Description

METHOD AND SYSTEM FOR NOISE STANDARD DEVIATION ESTIMATION

BACKGROUND

[0001] Standard deviation is a mathematical formula that shows how much variation exists in a set of data from its average. Standard deviation is often used to model noise. In noise reduction algorithms, such as non-local means de-noising algorithm, the noise standard deviation is an important parameter to control the amount of smoothing in the final reconstructed image. It is important to estimate local noise standard deviation accurately, otherwise the resulting noise reduced image may contain undesirable characteristics such as too much noise, a loss in resolution, and other artifacts. However, as the noise standard deviation is not uniform for different computed tomographic (CT) images, it is difficult to estimate noise standard deviation accuracy.

BRIEF DESCRIPTION

[0002] The present disclosure relates to a noise standard deviation estimation method. In the method, an input image containing noise is received and filtered to acquire a smoothed image. A noise map is generated as a difference between the input image and the smoothed image. An edge pre-removed noise map is acquired by pre -removing edges in the noise map. A threshold T or a threshold function T_g is estimated from the edge pre-removed noise map. Then the threshold T or threshold function T_g is used to identify edges in the noise map. An edge removed noise map is obtained by removing the identified edges from the noise map. Noise standard deviation is estimated from the edge removed noise map.

[0003] The present disclosure also relates to another noise standard deviation estimation method. In the method, an input image containing noise is received and filtered to acquire a smoothed image. A noise map is generated as a difference between the input image and the smoothed image. Noise standard deviation values of pixels in homogeneous tissue areas of the noise map are estimated, and then a noise standard deviation function is estimated with curve fitting technology based on the noise standard deviation values and coordinates of the pixels in the homogeneous tissue areas.

BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The above and other aspects and features of embodiments of the present disclosure will become more apparent in light of the subsequent detailed description when taken in conjunction with the accompanying drawings in which:

[0005] FIG. 1 is a drawing of an embodiment of a CT imaging apparatus.

[0006] FIG. 2 is a pictorial block diagram of the CT imaging apparatus of

FIG. 1.

[0007] FIG. 3 is a flow chart of a standard deviation estimation method according to one embodiment of the present disclosure.

[0008] FIG. 4 is a flow chart of a standard deviation estimation method according to another embodiment of the present disclosure.

[0009] FIG. 5 is a flow chart of a standard deviation estimation method according to yet another embodiment of the present disclosure.

[0010] FIG. 6(a) shows a noisy image filtered by non-local means algorithm with local noise standard deviation (STD) estimated by a method proposed in this disclosure.

[0011] FIG. 6(b) shows a noisy image filtered by non-local means algorithm with noise STD of 90HU for the whole image.

[0012] FIG. 6(c) shows a noisy image filtered by non-local means algorithm with noise STD of 110HU.

[0013] FIG. 6(d) shows a noisy image filtered by non-local means algorithm with noise STD of 120HU. DETAILED DESCRIPTION

[0014] Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as "about," is not to be limited to the precise value specified. In certain embodiments, the term "about" means plus or minus ten percent (10%) of a value. For example, "about 100" would refer to any number between 90 and 110. Additionally, when using an expression of "about a first value - a second value," the about is intended to modify both values. In some instances, the approximating language may correspond to the precision of an instrument for measuring the value or values.

[0015] Unless defined otherwise, technical and scientific terms used herein have the same meaning as is commonly understood by one of skill in the art to which this invention belongs. The terms "first," "second," and the like, as used herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Also, the terms "a" and "an" do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced items.

[0016] A standard deviation estimation method is provided. The standard deviation estimated by the disclosed method is generally applicable to noise reduction algorithms for various CT imaging systems, such as a CT imaging system described in commonly assigned US7,706,497 entitled "Methods and apparatus for noise estimation for multi-resolution anisotropic diffusion filtering", filed on March 14, 2008.

[0017] FIG. 1 is a pictorial view of a CT imaging system 10. FIG. 2 is a block schematic diagram of system 10 illustrated in FIG. 1. In the exemplary embodiment, a computed tomography (CT) imaging system 10, is shown as including a gantry 12 representative of a "third generation" CT imaging system. Gantry 12 has a radiation source 14 that projects a cone beam 16 of X-rays toward a detector array 18 on the opposite side of gantry 12. [0018] Detector array 18 is formed by a plurality of detector rows (not shown) including a plurality of detector elements 20 that together sense the projected X-ray beams that pass through an object, such as a medical patient 22. Each detector element 20 produces an electrical signal that represents the intensity of an impinging radiation beam and hence the attenuation of the beam as it passes through the object or patient 22. During a scan to acquire radiation projection data, gantry 12 and the components mounted thereon rotate about a center of rotation 24. FIG. 2 shows only a single row of detector elements 20 (i.e., a detector row). However, multislice detector array 18 includes a plurality of parallel detector rows of detector elements 20 such that projection data corresponding to a plurality of quasi-parallel or parallel slices can be acquired simultaneously during a scan.

[0019] Rotation of gantry 12 and the operation of radiation source 14 are governed by a control mechanism 26 of CT system 10. Control mechanism 26 includes a radiation controller 28 that provides power and timing signals to radiation source 14 and a gantry motor controller 30 that controls the rotational speed and position of gantry 12. A data acquisition system (DAS) 32 in control mechanism 26 samples analog data from detector elements 20 and converts the data to digital signals for subsequent processing. An image reconstructor 34 receives sampled and digitized radiation data from DAS 32 and performs high-speed image reconstruction. The reconstructed image is applied as an input to a computer 36 that stores the image in a mass storage device 38.

[0020] Computer 36 also receives commands and scanning parameters from an operator via console 40 that has a keyboard and/or other user input device(s). An associated display system 42 allows the operator to observe the reconstructed image and other data from computer 36. The operator supplied commands and parameters are used by computer 36 to provide control signals and information to DAS 32, radiation controller 28 and gantry motor controller 30. In addition, computer 36 operates a table motor controller 44 that controls a motorized table 46 to position patient 22 in gantry 12. Particularly, table 46 moves portions of patient 22 through gantry opening 48. [0021] In one embodiment, computer 36 includes a device 50, for example, a floppy disk drive, CD-ROM drive, or DVD-ROM drive, for reading instructions and/or data from a computer-readable medium 52, such as a floppy disk, CD-ROM, or DVD. It should be understood that other types of suitable computer-readable memory are recognized to exist (e.g., CD-RW and flash memory, to name just two), and that this description is not intended to exclude any of these. In another embodiment, computer 36 executes instructions stored in firmware (not shown). Generally, a processor in at least one of DAS 32, reconstructed 34, and computer 36 shown in FIG. 2 is programmed to execute the methods/processes described below. Of course, the method is not limited to practice in CT system 10 and can be utilized in connection with many other types and variations of imaging systems. In one embodiment, computer 36 is programmed to perform functions described herein, accordingly, as used herein, the term computer is not limited to just those integrated circuits referred to in the art as computers, but broadly refers to computers, processors, microcontrollers, microcomputers, programmable logic controllers, application specific integrated circuits, and other programmable circuits.

[0022] The computer 36 may be programmed to perform noise standard deviation estimation, which will be described in details hereafter below.

[0023] In an aspect, a noise standard deviation estimation method capable of estimating noise standard deviation accurately is provided. As the method is particularly applicable in non-local means de-noising algorithms, the description is directed to non-local means de-noising algorithms, but can be used in other algorithms involving noise standard deviation estimation, such as bilateral filtering.

[0024] In certain embodiments, a noise standard deviation estimation method is provided based on reconstructed images. An original image containing noise, I_n, is input and filtered by a low pass filter to acquire a smoothed image I_s, which is an estimation of a noise free image. As used herein, the "low-pass filter" is an electronic filter that passes low-frequency signals and attenuates signals with frequencies higher than a cutoff frequency. The difference between I_n and I_s is denoted as N_e and considered as a noise map of the input image (original image). N_e = Is - In

[0025] The noise map N_e contains not only noise of the input image but also edges of structures that are present in the input image I_n but are smoothed out in the smoothed image I_s. If noise standard deviation is estimated based on the noise map N_e that contains edges, accuracy of the estimation may be affected by inaccuracies caused by these edges. Therefore, it is better to clearly remove edges in the noise map N_e before noise standard deviation estimation.

[0026] Generally, edge pixels have larger absolute noise values compared with non-edge pixels in the noise map N_e. One or more thresholds or a threshold function may be estimated and used to identify edges in the noise map N_e , by comparing the absolute noise values of pixels in the noise map N_e with the thresholds or threshold function.

[0027] In some embodiments, a threshold is estimated for the whole noise map N_e and used to identify edges by comparing the absolute noise value of each pixel in the noise map N_e with the threshold. Given that P_j represents the absolute noise value of a particular pixel in N_e and T is the threshold, if Pj > nT, the pixel is treated as an edge pixel and will be removed from the noise map N_e before noise standard deviation estimation. In this comparison, n is a constant scaling value for controlling the edge removal strength.

[0028] In consideration of the noise non-uniformity of CT images, the noise standard deviation usually varies with the positions in the image. In most cases, the threshold is not a fixed value for the whole noise map, but varies with the positions in the map. Therefore, in some embodiments, the noise map N_e is divided into N blocks or N*N blocks. The shape of the blocks may be rectangle, circle, ring-shaped or adaptive to the shape of the object. A threshold T_j is estimated for each block and used for edge removal in its block.

[0029] After Tj is estimated for each block, it may be used directly or used to form a function of threshold for the whole noise map. In particular, a threshold function T_g is estimated from all the block threshold data using curve fitting technology. The threshold function T_g provides a threshold map corresponding to the noise map in a manner that, for each pixel (i, j) in the noise map N_e, there is a noise reference value in the threshold map T_g, which can be used as a comparison reference during edge identification. The noise reference value may be proportional to the threshold T_g(i,j). For example, in a specific embodiment, the noise reference value for pixel (i, j) is n * T_g(i, j), where T_g(i, j) is the threshold for pixel (i, j), and n is a constant scaling value. When a pixel in N_e has an absolute noise value larger than its corresponding noise reference value in threshold map, for example, when P(i, j) > n * T_g(i, j), the pixel is treated as an edge pixel and will be removed from the noise map N_e before noise standard deviation estimation.

[0030] The threshold T for the whole noise map or threshold T; for a block of the map may be estimated by different ways.

[0031] In one embodiment, in a method for estimating the threshold T, edges in the noise map are pre -removed based on prior knowledge about edges in the noise map N_e, such as the knowledge that edges in the noise map always happen near a bones-tissue or an air-tissue boundary, for example. By using the prior knowledge, the number e_N of possible edge pixels in the input image can be estimated. In particular, as to an input image I_n filtered with a low pass filter to get the noise free image I_s and further to get the noise map N_e as the difference between I_n and I_s, the edges in its noise map N_e are determined from the convolution of edges pixels with the filter kernel. The approximate number ea_N of edge pixels in N_e is estimated by the possible edge pixels number e_N and the kernel size k*k of the low pass filter. ea_N=k*e_N

[0032] Since the pixels with relatively larger absolute noise values are regarded as edges, once the approximate number ea_N of edge pixels is determined, it can be deduced that the ea_N pixels with the ea_N largest absolute noise values are edge pixels. The largest absolute noise values can be easily determined by ranking the absolute pixel values in the noise map from the highest to the lowest. After the edge pixels are determined, they are pre-removed from the noise map N_e. The edge pre -removed noise map is denoted as N_ep.

[0033] Then noise standard deviation around pixel (i, j) of I_n is pre-estimated from the edge pre-removed noise map N_ep by:

Sigma_p (i, j) = std(N_ep (i— w: i + w, j— w: j + w)) , where the "std" is the known function to compute standard deviations, and 2w+l is the width of neighborhood to compute the pre-estimated standard deviation wherein the w may be adaptive with reconstruction field of view (FOV). The pre-estimated standard deviation map Sigma_p may be computed on basis of each pixel in the image, or may be computed sparsely from the image.

[0034] Then the threshold T is estimated based on the pre-estimated standard deviation map Sigma_p . A median filter is applied to the map Sigma_p and the threshold T is computed as the median value of Sigma_p. As such, estimation for T is very stable.

T = median(Sigma_p)

[0035] When T is acquired, the edge pixels in the noise map N_e can be identified by the criterion as discussed above, i.e., a pixel in the noise map N_e with an absolute value Pj > nT is treated as an edge pixel. After edge pixels are identified and removed from the noise map N_e, an edge removed noise map N_er is acquired.

[0036] In the cases that the threshold is not a fixed value for the whole noise map but varies with the positions in the map, after edges are pre-removed from the noise map N_e based on prior knowledge by the method as discussed above, the edge pre-removed noise map N_ep is divided into blocks. Standard deviation map Sigma_p is pre-estimated for each block by the method as discussed above and a threshold T; is computed for the block as the median value of Sigma_p .

Tj = median(Sigma_{p j}) [0037] After the threshold data for all the blocks is obtained, a threshold function T_g can be estimated from all the block threshold data using curve fitting technology.

[0038] When T_g is acquired, the edge pixels in the noise map N_e can be identified by the criterion as discussed above, i.e., a pixel in the noise map N_e with an absolute noise value of P(i, j) > n * T_g(i, j) is treated as an edge pixel. After edge pixels are identified and removed from the noise map N_e, an edge removed noise map N_er is acquired.

[0039] As discussed above, pixels with relatively larger absolute noise values generally belong to edges. Additionally or alternatively, pixels with relatively larger gradient generally belong to edges. Therefore, as an additional or alternative method of identifying edges by comparing the absolute noise value of each pixel with a noise reference value, edges may be additionally or alternatively be identified by comparing noise gradients of each pixel with a gradient reference value that is proportional to the corresponding threshold. The gradients of a CT image in x and y direction are computed by:

[FX , FY] = gradient (In) .

[0040] In some embodiments, edges are identified by comparing the absolute noise value of each pixel with a noise reference value and comparing the noise gradients of each pixel with a gradient reference value. For example, in a specific embodiment, the edge pixels may be defined as:

1 if abs(Ne(i, j)) > n * T_g (i, j)

1 if abs(FX (i, j)) > m * T_g (i, j)

Edge _ In(i, j) = (1),

1 if abs(FY(i, j)) > m * T_g (i, j)

0 where "abs" is the absolute value function, "n" and "m" are constants, which may be different from or the same with each other. Pixels with Edge_I_n (i, j) equal to 1 are defined as edge pixels and removed. Thus, the edges in the noise map can be clearly removed to acquire an edge removed noise map N_er.

[0041] Based on the edge removed noise map N_er, an accurate noise standard deviation map Sigma can be obtained. In particular, the noise standard deviation around pixel (i, j) of I_n can be estimated from the edge removed noise map N_er by:

SigmaO, j) = std(N_er(i— w: i + w, j— w: j + w)) (2), where the "std" is the known function to compute standard deviations, and 2w+l is the width of neighborhood to compute the standard deviation wherein the w may be adaptive with reconstruction FOV. Similarly, the standard deviation map Sigma may be computed on basis of each pixel in the image or computed sparsely from the image.

[0042] In some embodiments, the noise standard deviation map Sigma obtained by the process above may be further banded by the threshold function T_g by:

!LT_g(i, j) if SigmaO, j) < LT_g(i, j)

HTg(i, j) if Sigma(i, j) > HT_g(i, j) (3),

Sigma(i, j) otherwise

where S(i, j) is the noise standard deviation around a pixel (i, j), T_g (i, j) is the threshold around the pixel (i, j), and L and H are a relatively lower and higher constant, respectively.

[0043] In another aspect, an alternative noise standard deviation estimation method is provided.

[0044] After an original image is input and filtered to get a smoothed image, a noise map N_e containing edges is generated by the afore-mentioned method as a difference between the input image and smoothed image. There are homogeneous areas in the noise map N_e and noise standard deviation estimated from a homogeneous area is accurate. In certain embodiments, only noise standard deviation values of pixels in homogeneous tissue area is estimated, and the bony structure and low attenuation structures are excluded from the noise standard deviation estimation because such estimation on bony structures and low attenuation structures may be unstable. Moreover, in order to get an accurate standard deviation estimation result, pixels in the air are also excluded, which is easy because the noise standard deviation in the air is much smaller than that in the scanned object.

[0045] In the noise map N_e, if a pixel (i, j) is in a homogeneous area, the mean value of its neighborhood will be relatively small in comparison to pixels at edges of bony structures and low attenuation structures. Thus, it may be determinable whether a pixel is in a homogeneous tissue area by comparing the noise mean value of the neighborhood of each pixel in the noise map with a threshold of noise mean value and comparing the noise mean value of the neighborhood of each pixel in the input image with an air threshold and a bone threshold. The pixel is identified as in a homogeneous tissue area if the noise mean value of its neighborhood in the noise map is smaller than the threshold of noise mean value and its noise mean value for its neighborhood in the input image is larger than the air threshold and smaller than the bone threshold. In a specific embodiment, as shown in the following equation, only noise standard deviation values of pixels in homogeneous tissue areas are estimated. If a pixel belongs to tissue and it is in a homogeneous area, its standard deviation value is estimated, otherwise its standard deviation value is set as zero.

Simga_e (i,j) =

! , _Λ (if mean(N_e (i— w: i + w,j— w:j + w)) < t_n, and stdtN_e {i—w. i + w,j— w. j + w)) < , .

{ t_a < mean(I_n(i—w: i + w,j— w: j + w)J < t_b > 0 otherwise where t_n is a threshold of noise mean value, t_a is a threshold for air and t_¾ is a threshold for bone.

[0046] Based on the estimated noise standard deviation values of pixels in the homogeneous tissue areas (non-zero values of Sigma_e) and coordinates (i, j) of these pixels, a noise standard deviation function (map) can be estimated with curve fitting technology. In this embodiment, in the matrix Sigma_e , the non-zero standard deviation values are very close to the true noise standard deviation. As the noise standard deviation map is a quite smooth map, a surface may be estimated using curving fitting technology to fit the non-zero pixels in Sigma_e to obtain a noise standard deviation map represented by a function of noise standard deviation. For example, with polynomial curve fitting technology, a general Gaussian function that fits these measurements may be estimated. However, the noise standard deviation function is not limited to general Gaussian functions, and it could be a smooth surface that fits the noise standard deviation measurements in the homogeneous tissue areas.

[0047] As to a noise map generated from a very homogeneous original image, it's difficult to find a homogeneous area because there is no obvious boundary between homogeneous and heterogeneous areas. In this situation, the size of the neighborhood may be reduced to make it easier to find the homogeneous area for noise standard deviation estimation. For example, the parameter w used in the above equation of Sigma_e may be set as 1. As such, the size of neighborhood is 3*3, which may be small enough for facilitating homogeneous area identification.

[0048] In some embodiments, after the noise standard deviation function is estimated by above-described methods, it may be directly applied to a noise reduction algorithm.

[0049] In some other embodiments, the noise standard deviation function may be used as the threshold function T_g to identify edges in the noise map with the equation (1) above, and thereby remove the identified edges from the noise map. After the edges are removed from the noise map, noise standard deviation can be estimated by the equation (2) above based on the edge removed noise map. The noise standard deviation map estimated from the edge removed noise map may be directly used as the output noise map or further banded by the threshold function T_g with the equation (3) above before being output. Compared with directly applying the noise standard deviation function to a noise reduction algorithm, using it as the threshold function T_g to identify and remove edges in the noise map and then estimating noise standard deviation map from the edge removed noise map may increase the accuracy of noise standard deviation estimation.

[0050] After the noise standard deviation is estimated by above-described methods, it may be applied to a noise reduction algorithm. In certain embodiments, the estimated noise standard deviation is applied to a non-local means de-noising algorithm.

[0051] Referring to FIG. 3, a noise standard deviation estimation method includes receiving an input image containing noise in step Sl l, filtering the input image to acquire a smoothed image in step S12, and generating a noise map as a difference between the input image and the smoothed image in step SI 3. Edges in the noise map are pre -removed in step S14. A threshold T or a threshold function T_g is estimated from the edge pre-removed noise map in step S15. The threshold T or threshold function T_g is used to identify edges in the noise map in step SI 6. The identified edges are removed from the noise map in step S17. The noise standard deviation is estimated from the edge removed noise map in step S18.

[0052] In certain embodiments, in the step S14, the possible number e_N of edge pixels in the input image can be estimated based on prior knowledge about the edges. As mentioned above, as to an input image I_n filtered with a low pass filter to get the noise free image I_s and further to get the noise map N_e as the difference between I_n and I_s, the edges in the noise map N_e are determined from the convolution of edges pixels with the filter kernel. Thus, the approximate number ea_N of edge pixels in the noise map N_e is determined by e_N and the window size (k*k) of the low pass filter, and can be calculated by: ea_N =k*e_N.

[0053] As mentioned above, edge pixels generally have larger absolute noise values compared with non-edge pixels in the noise map N_e. Thus, the number of edge pixels, ea_N having the corresponding largest absolute values, that is the largest ea_N absolute values are considered as the edge pixels and removed. For example, once the number of edge pixels is estimated, e.g., 100, in the noise map, based on the premise that the pixels with relatively larger absolute noise values are edge pixels, it can be determined that the 100 pixels associated with the 100 largest absolute noise values are edge pixels and will be removed. As for a noise map N_e containing ea_N edge pixels, the pixels with the ea_N largest absolute noise values are edge pixels. By ranking pixels in the noise map in the order of their absolute noise values and removing the ea_N pixels with the ea_N largest absolute noise values, the edges in the noise map are pre-removed from the noise map.

[0054] In certain embodiments, in the step SI 5, a threshold T is estimated from the edge pre-removed noise map as a median value of noise standard deviation pre-estimated from the edge pre-removed noise map. When the threshold T is used to identify edges in the noise map in step SI 6, by comparing the noise value of each pixel in the noise map with a noise reference value proportional to the threshold T, pixels with an absolute noise value larger than the noise reference value are identified as the edge pixels.

[0055] In certain embodiments, in the step S15, the edge pre-removed noise map is divided into blocks and a threshold T; is computed for each block as a median value of noise standard deviation pre-estimated from the block. In certain embodiments, when the threshold function T_g is used to identify edges in the noise map in step SI 6, pixels with an absolute noise value larger than a noise reference value proportional to the corresponding threshold are identified as the edge pixels. In certain embodiments, when the threshold function T_g is used to identify edges in the noise map in step S16, pixels with an absolute noise value larger than a noise reference value proportional to the corresponding threshold and pixels with at least one noise gradient larger than a gradient reference value proportional to the corresponding threshold are identified as the edge pixels.

[0056] Referring to FIG. 4, a noise standard deviation estimation method includes receiving an input image containing noise in step S21, filtering the input image to acquire a smoothed image in step S22, and generating a noise map as a difference between the input image and the smoothed image in step S23. Noise standard deviation values of pixels in homogeneous tissue areas of the noise map are estimated in step S24. Then a noise standard deviation function is estimated with curve fitting technology in step S25 based on the noise standard deviation values of the pixels in the homogeneous tissue areas obtained in step S24 and coordinates of these pixels. [0057] Referring to FIG. 5, a noise standard deviation estimation method similar to that of FIG. 4 is provided. The difference is that after the noise standard deviation function is acquired, it is used as a threshold function to identify edges in the noise map in step S26. After the identified edges are removed from the noise map in step S27, noise standard deviation is estimated from the edge removed noise map in step S28. Similar to step S16 of FIG. 3, in certain embodiments, in step S26, pixels with an absolute noise value larger than the corresponding noise reference value or pixels with at least one noise gradient larger than the corresponding gradient reference value are identified as the edge pixels.

[0058] The methods of the embodiments as discussed above are capable of improving the accuracy of noise standard deviation estimation. A comparison example is shown in FIG. 6 to compare results of experiments where noisy CT images are filtered by non-local means algorithm with different parameter settings. FIG. 6(a) shows a noisy image filtered by non-local means algorithm with local noise standard deviation (STD) estimated by a method proposed in this disclosure. FIG. 6(b) shows a noisy image filtered by non-local means algorithm with noise STD of 90HU for the whole image. Compared to FIG. 6(a), the center part is noisier because the STD of 90HU is smaller than the true noise STD and thus image was less filtered. FIGs. 6(c) and 6(d) show noisy images filtered by non-local means algorithm with noise STD of 110HU and 120HU, respectively. Compared to FIG. 6(a), edges are blurred because the noise STD of 110HU or 120HU is larger than the true local noise STD and therefore the images were over smoothed. This example indicates that the STD estimation method proposed in this disclosure provides more accurate noise STD, and thus enables better de-noising.

[0059] The invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects as illustrative rather than limiting on the invention described herein. The scope of embodiments of the invention is thus indicated by the appended claims rather than by the foregoing description, and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims

CLAIMS:

1. A method, comprising:

receiving an input image containing noise;

filtering the input image to acquire a smoothed image;

generating a noise map as a difference between the input image and the smoothed image;

pre-removing edges in the noise map to acquire an edge pre-removed noise map;

estimating a threshold T or a threshold function T_g from the edge pre-removed noise map;

using the threshold T or threshold function T_g to identify edges in the noise map;

removing the identified edges from the noise map to obtain an edge removed noise map; and

estimating noise standard deviation from the edge removed noise map.

2. The method according to claim 1, wherein the pre-removing edges in the noise map comprises:

estimating a possible number e_N of edge pixels in the input image based on prior knowledge about the edges;

calculating an approximate number ea_N of edge pixels in the noise map from the number e_N of edge pixels in the input image; and

removing the ea_N pixels with the ea_N largest absolute noise values from the noise map.

3. The method according to claim 1, wherein a threshold T is estimated from the edge pre-removed noise map by a process comprising: pre-estimating noise standard deviation from the edge pre -removed noise map; and

computing the threshold as a median value of the noise standard deviation pre- estimated from the edge pre-removed noise map.

4. The method according to claim 3, wherein the using the threshold T to identify edges in the noise map comprises:

comparing the absolute noise value of each pixel in the noise map with a noise reference value proportional to the threshold T; and

identifying the pixel as an edge pixel if its absolute noise value is larger than the noise reference value.

5. The method according to claim 1, wherein a threshold function T_g is estimated from the edge pre-removed noise map by a process comprising:

dividing the edge pre-removed noise map into blocks;

pre-estimating noise standard deviation from each block and computing a block threshold T; as a median value of the noise standard deviation pre-estimated from the block; and

estimating a threshold function T_g based on the threshold data of the blocks.

6. The method according to claim 5, wherein the using the threshold function T_g to identify edges in the noise map comprises:

comparing the absolute noise value of each pixel in the noise map with a noise reference value proportional to the threshold for the pixel; and

7. The method according to claim 5, wherein the using the threshold function T_g to identify edges in the noise map comprises:

comparing the absolute noise value of each pixel in the noise map with a noise reference value proportional to the threshold for the pixel;

comparing one or more noise gradients of each pixel in the noise map along one or more directions, with a gradient reference value proportional to the threshold for the pixel; and

identifying the pixel as an edge pixel if its absolute noise value is larger than the noise reference value or at least one of its noise gradients is larger than the gradient reference value.

8. A non- transitory machine-readable medium having recorded thereon computer-readable instructions of a computer program that, when executed by a processor, cause the processor to perform a method, the method comprising:

receiving an input image containing noise;

filtering the input image to acquire a smoothed image;

pre-removing edges in the noise map to acquire an edge pre-removed noise map;

estimating noise standard deviation from the edge removed noise map.

9. The non-transitory computer-readable medium according to claim 8, wherein the pre-removing edges in the noise map comprises:

calculating an approximate number ea_N of edge pixels in the noise map from the number e_N of edge pixels in the input image ; and

removing the ea_N pixels with the ea_N largest absolute noise values.

10. The non-transitory computer-readable medium according to claim 8, wherein a threshold T is estimated from the edge pre-removed noise map in the method, by:

pre-estimating noise standard deviation from the edge pre-removed noise map; and

11. The non-transitory computer-readable medium according to claim 8, wherein a threshold function T_g is estimated from the noise map in the method, by: dividing the edge pre-removed noise map into blocks;

estimating a threshold function T_g based on the threshold data of the blocks.

12. A medical imaging apparatus, comprising: a radiation source and a radiation detector on a rotating gantry, the radiation detector configured to receive radiation from the radiation source through an object being scanned;

a data acquisition system configured to receive data from the radiation detector when the medical imaging apparatus is scanning an object and to provide projection datasets to a computer;

a display responsive the computer for displaying images produced by the computer from the projection datasets; and

a processor configured to: receive an input image containing noise; filter the input image to acquire a smoothed image; generate a noise map as a difference between the input image and the smoothed image; pre-remove edges in the noise map; estimate a threshold T or a threshold function T_g from the edge pre- removed noise map; use the threshold T or threshold function T_g to identify edges in the noise map; remove the identified edges from the noise map; and estimate noise standard deviation from the edge removed noise map.

13. A method, comprising:

receiving an input image containing noise;

filtering the input image to acquire a smoothed image; generating a noise map as a difference between the input image and the smoothed image;

estimating noise standard deviation values of pixels in homogeneous tissue areas of the noise map; and

estimating a noise standard deviation function with curve fitting technology based on the noise standard deviation values of the pixels in the homogeneous tissue areas and coordinates of these pixels.

14. The method according to claim 13, wherein the homogeneous tissue areas exclude air and bone areas.

15. The method according to claim 13, wherein pixels in the noise map are identified as in homogeneous tissue areas by:

comparing the noise mean value of neighborhood of each pixel in the noise map with a threshold of noise mean value;

comparing the noise mean value of neighborhood of each pixel in the input image with at least a threshold for air and a threshold for bone.

identifying the pixel as in a homogeneous tissue area if the noise mean value of its neighborhood in the noise map is smaller than the threshold of noise mean value and its oise mean value for its neighborhood in the input image is larger than the threshold for air and smaller than both the threshold for bone.

16. The method according to claim 13, wherein the noise standard deviation function is acquired by using a general Gaussian function to fit the coordinates of the pixels in the homogeneous tissue areas and their noise standard deviation values.

17. The method according to claim 13, further comprising: using the noise standard deviation function as a threshold function to identify edges in the noise map;

removing the identified edges from the noise map; and

estimating noise standard deviation from the edge removed noise map.

18. The method according to claim 17, wherein the using the noise standard deviation function as a threshold function to identify edges in the noise map comprises:

identifying the pixel as an edge pixel if its absolute noise value is larger than the noise reference value or at least one of its noise gradient is larger than the gradient reference value.

19. A non-transitory machine-readable medium having recorded thereon computer-readable instructions of a computer program that, when executed by a processor, cause the processor to perform a method, the method comprising:

receiving an input image containing noise;

filtering the input image to acquire a smoothed image;

estimating noise standard deviation values of pixels in homogeneous tissue areas of the noise map; and estimating a noise standard deviation function with curve fitting technology based on the noise standard deviation values of the pixels in the homogeneous tissue areas and coordinates of these pixels.

20. The non-transitory computer-readable medium according to claim 19, wherein the method further comprises:

using the noise standard deviation as a threshold function to identify edges in the noise map;

estimating noise standard deviation from the edge removed noise map.

21. A medical imaging apparatus, comprising:

a radiation source and a radiation detector on a rotating gantry, the radiation detector configured to receive radiation from the radiation source through an object being scanned;

a processor configured to: receive an input image containing noise; filter the input image to acquire a smoothed image; generate a noise map as a difference between the input image and the smoothed image; estimate noise standard deviation values of pixels in homogeneous tissue areas of the noise map; and estimate a noise standard deviation function with curve fitting technology based on the noise standard deviation values of the pixels in the homogeneous tissue areas and coordinates of these pixels.

22. The medical imaging apparatus of claim 21, wherein the processor is further configured to:

use the noise standard deviation as a threshold function to identify edges in the noise map;

remove the identified edges from the noise map to obtain an edge removed noise map; and

estimate noise standard deviation from the edge removed noise map.