Method for estimating parameters and method for removing objects from digital images

Abstract

The present invention provides a method for estimating parameters and a method for removing objects from digital images. The method for estimating parameters includes at least the following steps: a) an initial step of creating a content component dictionary product and an object component dictionary product, wherein the content component and the object component have the same scale as the digital image; b) a step of jointly determining the amplitude of each component in the content component dictionary and the object component in the object component dictionary present in the digital image; c) determining the value of at least one parameter characterizing the object to be estimated based on the amplitude of each object component in the object component.

Description

Technical Field

[0001] The invention relates to a method for estimating parameters of an object to be estimated in a digital image and to a method for removing an object from a digital image. The invention is particularly applicable to digital images obtained by X-ray imaging, but can be extended to any type of digital imager, for example, a digital imager imaging infrared radiation or even light in the visible spectrum. Background Art

[0002] In this patent application, there may be three components in a digital image:

[0003] 1. Clinical content or context corresponding to the real object being imaged that one is trying to view. This can be problematic, for example, in the case of X-ray imaging of a patient or a part of a patient's body.

[0004] 2. Acquisition noise corresponding to random perturbations in forming the image. This can be electronic noise that must be added to the image in X-ray imaging, photon noise due to the small number of photons present in the image, and a problem that follows a Poisson distribution.

[0005] 3. Seeking an estimated object that may prove harmful to the viewing of the content.

[0006] The digital image can then be written in two different ways, depending on whether the noise is treated independently of the other two components:

[0007] Image = object + content + noise

[0008] Still considered as content:

[0009] Image = object + content

[0010] Figure 1 An example of an image containing an object to be estimated is shown. In the present case, the figure shows a radiological image, the content of which is a body part of a patient. In order to improve the contrast of the image, especially the quality of radiological images, practitioners usually use an anti-scatter grid. The anti-scatter grid is located between the patient and the detector, and it can reduce the radiation scattered and caused by the patient. Figure 1 In the digital image, level variations are thus attributed to the presence of the anti-scatter grid; these variations may obscure a large amount of information and potentially lead to a poor diagnosis. Image processing must therefore be applied in order to remove these level variations from the digital image without modifying the content.

[0011] However, this process faces two major difficulties. First, it must be possible to remove only the object, even if the image also contains noise, and even if the content may be a very strong and unpredictable signal. In particular, the content varies greatly depending on the part of the patient's body to be imaged, and for a given body part, the content may vary from patient to patient. Another difficulty is due to the fact that the object to be estimated is not perfectly defined, i.e., many parameters of the object may not be known. Figure 2 Another example of an object to be estimated is shown. This is the problem of superimposing a square CR on the image IM, which prevents a correct viewing of the content. Neither the amplitude of the object (the value of the pixel, for example the grayscale of a radiological image) nor the size of the object is known.

[0012] Currently, two types of solutions allow processing a signal in order to remove undesired components therefrom.

[0013] A first class of solutions encompasses conventional filters, in particular matched filters, Wiener filters or even Kalman filters. These solutions are based on the estimation and statistical modeling of the content and of a signal that prevents its estimation (usually a random noise that is decorrelated with the content). In our case, the content (the patient) is not modelable, but still represents the majority of the signal present in the image. Therefore, such solutions can be implemented in "flat" areas of the image, where the patient is not present, but remain suboptimal when the patient is present. In addition, these solutions have the following disadvantages: for example, if the image contains components similar to the object to be removed, then removing the object will more or less modify the content of the image. Reference Figure 1 , if there is a feature similar to the anti-scatter grid in the content acquired by the detector, it may be removed if a matched filter is used.

[0014] The second solution covers spectrum estimation methods, in particular the IAA method (IAA is the acronym for iterative adaptive method) described in detail in the paper "Source localization and sensing: A nonparametric Iterative Adaptive Approach based on weighted least squares" (Yardibi T. et al., Aerospace and Electronic Systems, IEEE Transactions on 46.1 2010), and the SLIM method (SLIM is the acronym for sparse learning via iterative minimization) described in detail in the paper "Sparse Learning via Iterative Minimization with application to MIMO Radar Imaging" (Tan X. et al., IEEE Transactions on Signal Processing, vol. 59, no. 3, March 2011). These methods are applicable to the radar and telecommunication fields, where the signal is one-dimensional but cannot be transposed into a two-dimensional signal in the prior art, and is therefore used for image processing. In addition, in the SLIM method, the noise is assumed to be white noise. This assumption cannot be used for images acquired by the detector, in which case the noise is specific to each imaging technology. In particular, in X-ray imaging, photon noise is not white noise.

[0015] Finally, the aforementioned methods only consider two signals, namely, content and noise. Therefore, they do not allow the estimation of one or more parameters of objects that hinder the viewing of the content and are different from the acquisition noise. Summary of the invention

[0016] The present invention therefore aims at obtaining a method for estimating one or more parameters of an object to be estimated in a digital image, this object being different from the acquisition noise, said method not requiring the precise prior knowledge of the content, or the object to be estimated, or the acquisition noise. The invention also relates to a method for removing an object from a digital image, which method does not modify in the image the content corresponding to the real object imaged.

[0017] Therefore, an object of the present invention is to provide a method for estimating one or more parameters of an object to be estimated in a digital image representing real content of imaging, the method comprising at least:

[0018] a) comprising the initial steps of creating a content component dictionary and creating an object component dictionary, said content components and said object components having the same size as said digital image;

[0019] b) a step of jointly determining the magnitude of each of the content components in the content component dictionary and the object components in the object component dictionary present in the digital image;

[0020] c) A step of determining a value of at least one parameter characterizing the object to be estimated based on the amplitude of each of the object components.

[0021] Advantageously, the step c) of determining the value of at least one parameter characterizing the object to be estimated comprises the following sub-steps:

[0022] - determining the subset of object components having the highest amplitude;

[0023] - determining the value of said parameter according to a linear combination of the object components in said subset.

[0024] Advantageously, creating said content dictionary comprises generating a set of images of two-dimensional sinusoidal signals.

[0025] As a variant, creating the content dictionary comprises generating a set of images representative of the modulation transfer function of the sensor forming the digital image.

[0026] As a variant, the content dictionary is created using a machine learning algorithm.

[0027] Advantageously, the machine learning algorithm is a K-SVD algorithm.

[0028] Advantageously, creating said object component dictionary comprises generating a set of images having different values ​​of said parameter.

[0029] Advantageously, said parameter is selected from the group consisting of frequency, shape, size and position of said object.

[0030] Advantageously, the joint determination step b) is performed by iteratively determining an estimation vector (β) containing different amplitude values ​​of respective ones of the components of the content dictionary and the components of the object dictionary present in the image until said estimation vector (β) converges.

[0031] Advantageously, the estimated vector (β) is considered to have converged when the norm of the estimated vector (β) remains below a preset threshold for two consecutive iterations.

[0032] As a variant, at the end of a preset number of iterations, the estimation vector (β) is considered to have converged.

[0033] Advantageously, the method comprises, at the end of each iteration, the step of modifying the components in the content component dictionary and / or the components in the object component dictionary so as to minimize the projection error (ε) defined by:

[0034] ε=|y-Dβ| 2 ,

[0035] Wherein, y is a vector representing the digital image, and D is a matrix representing the dictionary components to be modified.

[0036] Advantageously, the joint determination step b) comprises iteratively determining the noise variance (σ 2 ) until the noise variance (σ 2 ) converges, the estimate of the noise variance being determined based on the estimation vector (β) and the correlation matrix N of the noise present in the digital image.

[0037] Advantageously, the correlation matrix N of the noise is determined via a priori knowledge of the detector used to acquire the digital image.

[0038] Advantageously, the method comprises a step d) of reconstructing a content image by a linear combination of all said content components.

[0039] Advantageously, the digital image is acquired by X-ray imaging.

[0040] The invention also relates to a method for removing an object present in a digital image representing an imaged real content, said method comprising the following steps:

[0041] - using the parameter estimation method, estimating the value of at least one parameter of the object and the amplitude of the object;

[0042] - based on the values ​​of the parameters characterizing the object and the magnitude of the object, estimating the object;

[0043] - Subtracting the estimated object from the digital image pixel by pixel. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Other features, details and advantages of the present invention will become more apparent from reading the description given with reference to the accompanying drawings, which are given as examples and which show respectively as follows:

[0045] - Already described Figure 1 is an example of oscillations present in an X-ray image and caused by the anti-scatter grid;

[0046] - Figure 2 is an example of an object to be estimated in a digital image;

[0047] - Figure 3 is a functional schematic diagram of the method according to the present invention;

[0048] - Figure 4A is an example of a content component dictionary, which is obtained based on Fourier components;

[0049] - Figure 4B is another example of a content component dictionary, which is obtained based on the impulse response of the detector;

[0050] - Figure 5 is an example of an object component dictionary for which the parameter to be estimated is the size of the square;

[0051] - Figure 6 is a schematic illustration of the various steps of an algorithm for jointly determining the magnitude of both an object component and a content component according to a first embodiment;

[0052] - Figure 7 is a schematic illustration of the various steps of an algorithm for jointly determining the magnitude of both an object component and a content component according to a second embodiment;

[0053] - Figure 8 is a graph illustrating the magnitude of each object component;

[0054] - Fig. 9 yes Figure 2 An image from which the object has been removed. DETAILED DESCRIPTION

[0055] Figure 2 A digital image IM is illustrated, which contains an object (square CR) that makes the corresponding part of the digital image white. Figure 2 In , for the sake of clarity of the drawing, only the dotted line around the square CR is shown. It is therefore sought to estimate the value of at least one parameter characterizing the object and the magnitude of the object, with the aim of estimating how much the square CR brightens the image.

[0056] Figure 3 A functional schematic diagram of the method according to the invention is illustrated.

[0057] The initial first step a) comprises creating a content component dictionary and creating an object component dictionary.

[0058] Therefore, the first sub-step consists in creating a content component dictionary.

[0059] According to a first embodiment, a content component dictionary may be created without prior knowledge by generating a set of images of elementary two-dimensional sinusoidal signals. Figure 4ASuch a dictionary is illustrated. Each of the content components (COMP_CONT_1, COMP_CONT_2, ..., COMP_CONT_K) (K being greater than or equal to 1) represents a two-dimensional sinusoidal signal, ie at a specific frequency. The illustrated content components are referred to as Fourier components. Figure 4A The number of content components shown in is non-limiting.

[0060] According to another embodiment, a content component dictionary may be created by generating a set of images representing the modulation transfer function of a sensor forming the digital image. Figure 4B Such a dictionary is illustrated. The dictionary is generated based on the impulse response of the detector. Each of the content components (COMP_CONT_1, COMP_CONT_2, ..., COMP_CONT_K) (K greater than or equal to 1) represents the impulse response of the detector for one pixel. Therefore, the content dictionary consists of the set of all these images for each pixel of the detector. This dictionary is advantageously close to the physical properties of the detector, especially in X-ray imaging.

[0061] According to another embodiment, a content component dictionary can be created using a machine learning algorithm, and in particular a K-SVD algorithm. The K-SVD algorithm is particularly suitable for creating and learning dictionary components, which makes it easy to implement. A content component dictionary using such an algorithm can, for example, create components from a set of radiographic images. Other machine learning algorithms can be used, for example, a neural network or even a SVM algorithm (SVM is an acronym for support vector machine).

[0062] The scale of each content component may be the same as the scale of the digital image in which the object is found. For example, if the object is very localized, parameter estimation may also be performed on a portion of the digital image. In this case, the scale of each content component is the same as the scale of the portion of the digital image.

[0063] The second sub-step of the initial first step a) comprises creating an object component dictionary. The object component dictionary can be created by generating a set of images with different values ​​of parameters. Non-exhaustively, the parameters can be the frequency, shape, size and position of the object.

[0064] Figure 5 shows an example of an object component dictionary for which the parameters to be estimated are Figure 2 The size of the square to be estimated in . Figure 5The number of object components (COMP_OBJ_1, COMP_OBJ_2, COMP_OBJ_3, COMP_OBJ_4) present in (i.e. the number of possible values ​​that the parameter to be estimated may take) is non-limiting. It may in particular comprise as many components as squares of different sizes (e.g. 1×1 pixels, 2×2 pixels, 3×3 pixels, etc.) in the digital image.

[0065] The most common case is when there is one parameter to be estimated (e.g., the size of a square) and the corresponding object magnitude. Therefore, the object component dictionary includes as many object components as there are possible values ​​for the parameter. The object component with the highest magnitude corresponds to the correct parameter value. It is also possible to envision a case where there are multiple parameters to be estimated (e.g., the position and size of a square) and the corresponding object magnitudes. If the object is the sum of known components whose magnitudes are unknown, the magnitudes of each of these components must be estimated.

[0066] Thus, a content component dictionary and an object component dictionary are obtained. Each component is a matrix of I rows and J columns written in vector form of size M, M being the size of the image, or the size of the part of the image where the object is found (ie all corresponding pixels).

[0067] According to the two embodiments described below, the magnitudes of the content components in the content component dictionary and the object components in the object component dictionary present in the digital image can be jointly determined. Figure 3 Step b)) in the above.

[0068] First embodiment

[0069] In this first embodiment, the noise present in the digital image is processed separately from the content and objects. This separate processing can be justified based on the different properties of the processed data: the data of both content and objects are not random, while the data of noise is random.

[0070] Let D be a matrix of size M x L ​​containing the various components to be estimated (objects and content). Thus, the matrix D is the concatenation of the content component dictionary and the object component dictionary. L is the number of components in both the content component dictionary and the object component dictionary. D, which is a vector of size M i is the i-th component of the matrix D.

[0071] Information about the correlation of the noise present in the digital image is placed in a matrix N that is different from the matrix D. Therefore, the noise present in the digital image is treated separately from the content and the object. The correlation matrix N of the noise can be determined via a priori knowledge of the detector used to acquire the digital image. In particular, the noise may be unique to each imaging technology (X-ray, infrared, visible light). In particular, in X-ray imaging, photon noise is usually not white noise. The correlation matrix N of the noise can be estimated by performing an inverse Fourier transform on the spectral power density of a "monotonic" image (i.e., an image without content) using the Wiener-Khintchine theorem.

[0072] As a variant, if it is assumed that there is no correlation between pixels, N can be an identity matrix of size M×M.

[0073] Let y be a vector representing a digital image, ie, the value (also called brightness) of each pixel.

[0074] Let β be an estimation vector of size L, which contains the components D i Therefore, β=[β1,β2,…,β L ].

[0075] Let a, b and q be the parameters of the algorithm, a and b depend on the nature and knowledge of the noise. In particular, if nothing is known about the noise, then a=0 and b=0.

[0076] The algorithm for jointly determining the magnitude of each component in the content component dictionary and the object component dictionary present in the digital image comprises an initialization step and six iteration steps, such as Figure 6 shown.

[0077] Initialization steps

[0078] This can be done in any manner (e.g., using random values) or indeed by determining the individual components D i The scalar product between y and the vector representing the digital image is used to initialize the value of the estimated vector β:

[0079] β i =D i .y, where 1≤i≤L

[0080] Furthermore, the noise variance (σ) can be initialized in any manner (e.g., using a random value) or using the following relationship: 2 )’s estimate:

[0081]

[0082] β is at its initial value.

[0083] Iteration Steps

[0084] 1. Calculate P = |β| q Z, where q is a parameter set by the user; it is a real number between 1 and 2. The user can vary the value of this parameter depending on the final result (i.e., on how well the object is removed from the image). Z is a diagonal matrix to privilege the estimation of certain components - in the general case, Z will be the identity matrix. Z can be parameterized by the user.

[0085] 2. Calculate the estimated matrix R of the covariance matrix of the signal y of the digital image:

[0086] R=Ddiag(P)D H +σ 2 N

[0087] 3. Calculate the normalization term:

[0088] Nor=|β i | -q

[0089] 4. Next, use the following formula to calculate the component β i The estimated ranges of :

[0090]

[0091] 5. For example, the noise variance σ can be calculated using the following formula: 2 Estimates:

[0092]

[0093] 6. Optionally, the dictionary components can be modified to minimize the projection error ε defined by:

[0094] ε=|y-Dβ| 2

[0095] In particular, each dictionary component D can be updated using an update parameter λ between 0 and 1. i :

[0096]

[0097] in, is the dictionary component to be updated D i ,and is the updated dictionary component D i .

[0098] The update parameter λ may be set to 0; in this case, there are no updates to the components in the dictionary.

[0099] Other methods, in particular bisection or gradient descent, can be used to update the dictionary component D i .

[0100] The updating step may be applied to content components in the content component dictionary and / or object components in the object component dictionary.

[0101] These six steps are repeated until the algorithm converges, that is, until the estimated vector β and the noise variance σ 2 The estimate of converges. Since the noise variance σ 2 depends directly on β, so convergence of one implies convergence of the other.

[0102] When the norm of the estimated vector β remains below a preset threshold for two consecutive iterations and when the noise variance σ 2 When the estimated value of remains below the preset threshold for two consecutive iterations, the estimated vector β and the noise variance σ 2 The estimate of is considered to have converged.

[0103] As a variation, at the end of a preset number of iterations, convergence may be considered to have been reached. Then, the value of the one or more parameters of the object may be determined ( Figure 3 Step c) in the step c)). Step c) comprises the following sub-steps:

[0104] - determining the subset of object components having the highest amplitude;

[0105] - performing a linear combination of the object components in said subsets.

[0106] In particular, the subset of object components having the highest amplitude may comprise a single component.

[0107] Using the above algorithm, it is also possible to reconstruct the content corresponding to the real content of the image by performing linear combination of all content components ( Figure 3 This reconstruction makes it possible to obtain an image without noise.

[0108] Second embodiment

[0109] In this second embodiment, the noise present in the digital image is processed together with the content and objects (ie, in the same matrix).

[0110] With respect to the first embodiment, the matrix D is therefore the result of the juxtaposition of the object component dictionary, the content component dictionary and the information on the relevance of the noise present in the digital image (which information formed the matrix N in the first embodiment).

[0111] y is a vector representing the digital image, ie, the value of each pixel.

[0112] β is an estimation vector of size L, which contains the components D i Therefore, β=[β1,β2,…,β L ]. q is a parameter of the algorithm. Compared with the first embodiment, the noise variance σ is not calculated. 2 therefore, the parameters a and b were not used.

[0113] The joint determination algorithm also includes an initialization step and five iteration steps, such as Figure 7 shown.

[0114] Initialization steps

[0115] This can be done in any manner (e.g., using random values) or indeed by determining the individual components D i The value of the estimated vector β is initialized by the product of the vector y representing the digital image:

[0116] β i =D i .y, where 1≤i≤L

[0117] Iteration Steps

[0118] 1. Calculate P = |β| q Z, where q is a parameter set by the user; it is a real number between 1 and 2. The user can vary the value of this parameter depending on the final result (i.e., on how well the object is removed from the image). Z is a diagonal matrix to privilege the estimation of certain components - in the general case, Z will be the identity matrix. Z can be parameterized by the user.

[0119] 2. Calculate the estimated matrix R of the covariance matrix of the signal y of the digital image:

[0120] R=Ddiag(P)D H

[0121] 3. Calculate the normalization term:

[0122] Nor=D iH R -1 D i

[0123] 4. Next, use the following formula to calculate the component β i The estimated ranges of :

[0124]

[0125] 5. Optionally, the components of the dictionary can be modified to minimize the projection error ε in the same way as in the first embodiment:

[0126] These five steps are repeated until the algorithm converges, that is, until the estimated vector β converges.

[0127] When the norm of the estimated vector β remains below a preset threshold for two consecutive iterations, the estimated vector β may be considered to have converged.

[0128] As a variation, at the end of a preset number of iterations, it can be considered that convergence has been achieved. Step c) and step d) are the same as those in the first embodiment.

[0129] Third embodiment

[0130] In this third embodiment, noise, content and objects are processed separately. This separate processing can be justified based on the different properties of the processed data: noise is random, content is modeled by a content component dictionary, and objects are modeled by an object parameter component dictionary.

[0131] Let Dc be a matrix of size M×Lc containing the various components of the content to be estimated. Let Ds(μ) be a parameter matrix of size M×Ls containing the various components of the object to be estimated. The vector μ is a parameter selected from a set that non-exhaustively includes the frequency, shape, size, and position of the object. Lc is the number of components in the content component dictionary, and Lc is the number of components in the object component dictionary. Dc as a vector of size M i is the i-th component of the matrix Dc, and Ds is a vector of size M i (μ) is the i-th component of the matrix Ds(μ).

[0132] Let D be the matrix resulting from the concatenation of the object component dictionary Ds(μ) and the content component dictionary Dc.

[0133] Information about the correlation of the noise present in the digital image is placed in a matrix N that is different from the matrices Dc and Ds(μ). Therefore, the noise present in the digital image is treated separately from the content and the object. The correlation matrix N of the noise can be determined via a priori knowledge of the detector used to acquire the digital image. In particular, the noise may be specific to each imaging technology (X-ray, infrared, visible light). In particular, in X-ray imaging, photon noise is usually not white noise. The correlation matrix N of the noise can be estimated by taking an inverse Fourier transform of the spectral power density of a "monotonic" image (i.e., an image without content) using the Wiener-Hinchin theorem.

[0134] As a variant, if it is assumed that there is no correlation between pixels, N can be an identity matrix of size M×M.

[0135] Let y be a vector representing a digital image, ie, the value (also called brightness) of each pixel.

[0136] Let βc be a content estimate vector of size Lc, which contains the components Dc of the content i Therefore, βc=[βc1,βc2,…,βc Lc ].

[0137] Let βs be the object estimation vector of size Lc, which contains the components Ds of the object i (μ) is the estimated amplitude. Therefore, βs=[βs1,βs2,…,βs Ls ].

[0138] Let β be the vector resulting from the concatenation of a vector βs containing the magnitude of the object component and a vector βc containing the magnitude of the content component.

[0139] Let a, b and q be the parameters of the algorithm, a and b depend on the nature and knowledge of the noise. In particular, if nothing is known about the noise, then a=0 and b=0.

[0140] The algorithm for jointly determining the magnitude of each component in the content component dictionary and the object component dictionary present in the digital image comprises an initialization step and six iteration steps, such as Figure 6 shown.

[0141] Initialization steps

[0142] The individual components Dc may be determined in any manner (e.g., using random values) or in fact by determining i The value of the content estimation vector βc is initialized by the product of the vector y representing the digital image:

[0143] βc i =Dc i .y, where 1≤i≤Lc

[0144] The individual components Ds may be determined in any manner (e.g., using random values) or in fact by determining i The value of the object estimation vector βs is initialized by the product of the vector y representing the digital image:

[0145] βs i =Ds i (μ).y, where 1≤i≤Ls

[0146] Furthermore, the noise variance (σ) can be initialized in any manner (e.g., using a random value) or using the following relationship: 2 )’s estimate:

[0147]

[0148] βc and βs are at their initial values.

[0149] Iteration Steps

[0150] 1. Calculate P = |β| q Z, where q is a parameter set by the user; it is a real number between 1 and 2. The user can vary the value of this parameter depending on the final result (i.e., on how well the object is removed from the image). Z is a diagonal matrix to privilege the estimation of certain components - in the general case, Z will be the identity matrix. Z can be parameterized by the user.

[0151] 2. Calculate the estimated matrix R of the covariance matrix of the signal y of the digital image:

[0152] R=Ddiag(P)D H +σ 2 N

[0153] 3. Calculate the normalization term:

[0154] Nor=|β i | -q

[0155] 4. Next, use the following formula to calculate the component β i The estimated ranges of :

[0156]

[0157] 5. For example, the noise variance σ can be calculated using the following formula: 2 Estimates:

[0158]

[0159] 6. Optionally, the object dictionary components can be modified to minimize the projection error ε defined by:

[0160] ε=|y-Dcβc-Ds(μ)βs| 2

[0161] In particular, gradient descent can be used to update each dictionary component D with the new value of the parameter μ i To do this, we use J (called the Jacobian of the function |y-Dcβc-Ds(μ)βs| with respect to μ):

[0162]

[0163] Then, the new value of the parameter μ is given by

[0164] μ new =μ old +[J T ×J] -1 ×J T ×|y-Dcβc-Ds(μ)βc|

[0165] These six steps are repeated until the algorithm converges, that is, until the estimated vector β and the noise variance σ 2 The estimate of converges. Since the noise variance σ 2 depends directly on β, so convergence of one implies convergence of the other.

[0166] When the norm of the estimated vector β remains below the preset threshold for two consecutive iterations and when the noise variance σ 2 When the estimated value of remains below the preset threshold for two consecutive iterations, the estimated vector β and the noise variance σ 2 The estimate of is considered to have converged.

[0167] As a variation, at the end of a preset number of iterations, convergence may be considered to have been reached. Then, the value of the one or more parameters of the object may be determined ( Figure 3 Step c) in the step c)). Step c) comprises the following sub-steps:

[0168] -Determine the value of μ.

[0169] Using the above algorithm, it is also possible to reconstruct the content corresponding to the real content of the image by performing linear combination of all content components ( Figure 3 This reconstruction makes it possible to obtain an image without noise.

[0170] The invention also relates to a method for removing an object present in a digital image representing an imaged real content, said method comprising the following steps:

[0171] - using the aforementioned parameter estimation method, estimating the value of at least one parameter of the object and the amplitude of the object;

[0172] - determining the object based on a parameter of the object and the magnitude of the object;

[0173] - Subtracting the object from the digital image pixel by pixel.

[0174] Using the first implementation of the algorithm, an estimate of the size and magnitude of the square can be obtained. Figure 8The result of executing the algorithm is shown. The parameter values ​​of the various components in the object dictionary are shown on the x-axis, and the estimated magnitude of each of these components is shown on the y-axis (in a logarithmic scale). It is clear from this figure that the algorithm has detected a square of size 7 with a high magnitude. Therefore, Figure 2 The width of the square in is 7, and the magnitude is 52. Using this information, the image can then be corrected to obtain a perfect correction, as Fig. 9 shown.

[0175] The method has been described for the entire image formed by the detector. The method can also be applied to a portion of the image formed by the detector by adapting the scale of the matrices and the scale of the vectors required to perform the parameter estimation.

[0176] The method has been described in the case of addition objects:

[0177] Image = object + content

[0178] The method can be applied to the case of multiplication of objects:

[0179] Image = object × content

[0180] For example, the anti-scatter grid is a multiplicative object, then the value of the frequency and its amplitude depends on the patient. To go from the additive case to the multiplicative case, it is sufficient to calculate the logarithm of the image (and thus the vector y):

[0181] (image) = log(object) + log(content)

[0182] Using the above addition method, to obtain the estimated vector β, we can estimate log(Object) and deduce from it:

[0183] Object = 10 log(对象)

[0184] The invention can be used in any process where it is necessary to improve the image quality. The method is particularly applicable to the field of medical imaging (X-ray, scanners, MRI, etc.) and any other type of imager (X-ray, visible light, infrared).

[0185] Specific applications include, for example:

[0186] -Remove perturbations that are distinct from noise and that reduce visibility and can lead to poor diagnosis in the case of medical imaging, e.g. Figure 1 The present invention advantageously allows noise to be left in the digital image, which may be desired by some medical imaging practitioners;

[0187] - Characterizing an object for technical or medical purposes (e.g., the size of a mass in a patient);

[0188] - Denoising: If the first embodiment is used, estimates of the object, content, and noise can be obtained (the noise variance σ is known). 2 The signal can then be reconstructed using only the object component and the content component. The same operation can be performed without the object to estimate only the content and noise.

[0189] Therefore, even if the dictionary contains many components, the method according to the invention is able to correctly estimate each component of the dictionary.The use of an iterative method allows the components to be estimated one by one, while each time filtering out as much as possible the other components estimated in advance.

Claims

1. A method for estimating one or more parameters of an object to be estimated in a digital image representing real content of an image, the method comprising at least the following steps: a) creating a content component dictionary and creating an object component dictionary, wherein the content component and the object component have the same scale as the digital image; b) jointly determining the magnitude of each of the content components in the content component dictionary and the object components in the object component dictionary present in the digital image, wherein the joint determination step b) is performed by iteratively determining an estimation vector (β) until the estimation vector (β) converges, the estimation vector comprising different amplitude values ​​of respective components of the components in the content component dictionary and the components in the object component dictionary present in the digital image; c) determining a value of at least one parameter characterizing the object to be estimated based on the amplitude of each of the object components, Wherein, step c) of determining the value of at least one parameter characterizing the object to be estimated comprises the following sub-steps: determining a subset of object components having the highest magnitude, wherein the object components having the highest magnitude correspond to correct parameter values; The value of the parameter is determined based on a linear combination of the object components in the subset.

2. The method according to claim 1, wherein: The step of creating a content component dictionary includes generating a set of images of two-dimensional sinusoidal signals.

3. The method according to claim 1, wherein: The step of creating a content component dictionary includes generating a set of images representing a modulation transfer function of a sensor that formed the digital image.

4. The method according to claim 1, wherein: The content component dictionary is created using a machine learning algorithm.

5. The method according to claim 4, wherein: The machine learning algorithm is the K-SVD algorithm.

6. The method according to claim 1, wherein: The step of creating an object component dictionary comprises generating a set of images each having a different value of the parameter.

7. The method according to claim 1, wherein: The parameter is selected from the group consisting of frequency, shape, size and position of the object.

8. The method according to claim 1, wherein: When the norm of the estimated vector (β) remains below a preset threshold for two consecutive iterations, the estimated vector (β) is considered to have converged.

9. The method according to claim 1, wherein: At the end of a preset number of iterations, the estimated vector (β) is considered to have converged.

10. The method according to claim 1, 8 or 9, comprising the step of modifying the components in the content component dictionary and / or the components in the object component dictionary at the end of each iteration so as to minimize the projection error (ε) defined by: ε=|y-Dβ| 2 , in, y is a vector representing the digital image, and D is a matrix representing the dictionary components to be modified.

11. The method according to claim 1, wherein: The joint determination step b) comprises iteratively determining the noise variance (σ 2 ) until the noise variance (σ 2 ) converges, the estimate of the noise variance being determined based on the estimation vector (β) and the correlation matrix N of the noise present in the digital image.

12. The method according to claim 11, wherein: The noise variance (σ 2 ) is defined by the following formula: Wherein, y is a vector representing the digital image, D is a matrix representing the dictionary components to be modified, N is the correlation matrix of the noise, M is the number of pixels in the digital image, and a and b are parameters determined according to the properties of the noise.

13. The method according to claim 1, wherein: The joint determination step (b) is performed by iteratively determining a vector resulting from the juxtaposition of a content estimation vector (βc) containing different estimated amplitude values ​​for each content component and an object estimation vector (βs), wherein the content estimation vector contains different estimated amplitude values ​​for each object component.

14. The method according to claim 13, comprising the following steps at the end of each iteration: modifying the components in the content component dictionary and / or the components in the object component dictionary to minimize the projection error (ε) defined by the following equation: ε=|y-Dcβc-Ds(μ)βs| 2 , in, y is a vector representing the digital image, Dc is a matrix representing the content component dictionary, and Ds(μ) is a matrix representing the object component dictionary.

15. The method according to claim 14, wherein: The joint determination step b) comprises iteratively determining the noise variance (σ 2 ), where the noise variance (σ 2 ) is defined by the following formula: Wherein, N is the correlation matrix of the noise, M is the number of pixels in the digital image, and a and b are parameters determined according to the properties of the noise.

16. The method according to claim 11, 12 or 15, wherein: The correlation matrix N of the noise is determined via a priori knowledge of the detector used to acquire the digital image.

17. The method according to claim 1, wherein: The method comprises a step d) of reconstructing the digital image of content via a linear combination of all the content components.

18. The method according to claim 1, wherein: The digital image is acquired by X-ray imaging.

19. A method of removing an object present in a digital image representing imaged real content, the method comprising the steps of: - using a method according to any one of claims 1 to 18, estimating the value of at least one parameter of the object and the amplitude of the object; - based on the value of the parameter characterizing the object and the magnitude of the object, estimating the object; - Subtracting the estimated object from the digital image pixel by pixel.

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