Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T5/00—Image enhancement or restoration
  • G06T5/70—Denoising; Smoothing
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T11/00—2D [Two Dimensional] image generation
  • G06T11/003—Reconstruction from projections, e.g. tomography
  • G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2207/00—Indexing scheme for image analysis or image enhancement
  • G06T2207/10—Image acquisition modality
  • G06T2207/10072—Tomographic images
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2207/00—Indexing scheme for image analysis or image enhancement
  • G06T2207/10—Image acquisition modality
  • G06T2207/10072—Tomographic images
  • G06T2207/10081—Computed x-ray tomography [CT]
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2211/00—Image generation
  • G06T2211/40—Computed tomography
  • G06T2211/408—Dual energy
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T2211/00—Image generation
  • G06T2211/40—Computed tomography
  • G06T2211/424—Iterative

Definitions

• the present invention relates to the field of iterative image reconstruction. Particularly, the present invention relates to a device and a method for denoising a vector- valued image.
• C i _1 is the inverse of the covariance matrix describing the noise between the material values of the material images (e.g., photo effect and Compton scatter) for the same image pixel i.
• ⁇ i,orig is a vector containing the different material values for pixel i of the input images, while contains the material values of the denoised images for pixel i.
• C i _1 is the inverse noise variance in each pixel.
• R ( ⁇ ) is a regularization term and ⁇ a regularization strength parameter.
• the terms with C i _1 reflect a model of correlated Gaussian noise in each pixel.
• US 2010/0220912 Al describes devices and methods for the noise reduction of CT image data with a scanning of an examination object and generation of at least two CT image data records each taking place on the basis of a different X-ray energy spectrum.
• US 2013/0343624 Al describes methods for reconstructing image component densities of an object including acquiring multi-spectral x-ray tomographic data, performing a material decomposition of the multi-spectral x-ray tomographic data to generate a plurality of material sinograms, and reconstructing a plurality of material component density images by iteratively optimizing a functional that includes a joint likelihood term of at least two of the material decomposed sinograms.
• An aspect of the present invention relates to device for denoising a vector- valued image.
• the device comprises a generator, a processor, and a noise-suppressor.
• the generator is configured to generate an initial loss function comprising at least one initial covariance matrix a model of correlated noise for each pixel of the vector- valued image.
• the processor is configured to provide a final loss function comprising a set of at least one final covariance matrix based on the initial loss function by modifying at least one submatrix and/or at least one matrix element of the initial covariance matrix.
• the noise-suppressor is configured to denoise the vector-valued image using the final loss function comprising the set of the at least one final covariance matrix.
• the present invention advantageously provides that false diagnostic results are avoided since denoising processing is improved.
• the present invention advantageously reduces the cross-talk by, for example, introducing frequency specific correlations between material values of one pixel or of subareas, i.e. image contents with low spatial frequency and high spatial frequency image contents can have different degree of correlation in the noise model.
• a further, second aspect of the present invention relates to a medical imaging system comprising a device according to the first aspect or according to any implementation form of the first aspect.
• a further, third aspect of the present invention relates to a method for denoising a vector-valued image, the method comprising the following steps of: - Generating an initial loss function comprising at least one initial covariance matrix defining a model of correlated noise for each pixel of the vector-valued image by means of a generator;
• Providing a final loss function comprising a set of at least one final covariance matrix based on the initial loss function by modifying at least one submatrix and/or at least one matrix element of the initial covariance matrix by means of a processor;
• the processor is configured to modify the at least one submatrix and/or the at least one matrix element of the initial covariance matrix by splitting the initial covariance matrix into two or more matrices, thereby providing the set in terms of at least two final covariance matrices based on at least two different spatial frequency bands of the vector-valued image. For example, the correlation in a low- frequency band of at least two different spatial frequency bands is lowered and therefore the crosstalk is advantageously reduced.
• the processor is configured to modify the at least one submatrix and/or the at least one matrix element of the initial covariance matrix, wherein the least two final covariance matrices are based on at least two different spatial frequency bands of the vector-valued image, defined by at least one high spatial frequency band and by at least one low spatial frequency band, wherein the high spatial frequency band comprises higher frequencies than the low spatial frequency band.
• the input covariance is split in two or more parts, so that a multitude of covariance matrices is provided.
• the images maybe for instance split into one image for high frequencies and image for low frequencies, and both are subject to denoising using the above set of individual covariance matrices, i.e. one matrix of the least two final covariance matrices is used for high frequencies and one matrix of the least two final covariance matrices is used for low frequencies.
• the processor is configured to provide the set of at the least final two covariance matrices based on a tuning between cross-talk removal and correlated noise removal of frequency noise. This advantageously allows an improved denoising performance.
• the generator is configured to generate the initial loss function by adding a regularization term to a matrix product of the at least one initial covariance matrix and the vector-valued image. This provides advantageously an improved correlated noise removal of frequency noise by adjusting the regularization term.
• the generator is configured to generate the initial loss function by adding the regularization term
• the generator is configured to generate the initial loss function comprising the at least one initial covariance matrix, which is constant for all pixel positions across the vector-valued image. This advantageously allows an improved denoising performance with reduced required computing power.
• the processor is configured to provide the final loss function comprising the final covariance matrix based on a splitting of the initial covariance matrix. This advantageously allows an improved denoising performance with reduced denoising artefacts.
• the processor is configured to provide the final loss function comprising the set of the at least one final covariance matrix based on the initial loss function by performing:
• the processor is configured to provide the final loss function comprising the set of the at least one final covariance matrix based on the initial loss function by reducing absolute values of off- diagonal elements of the initial covariance matrix at edges of material inhomogeneities of at least n materials of the vector-valued image.
• This advantageously provides a method to reduce the absolute values of off-diagonal elements in the co variance-matrices at edges of inhomogeneities in the material images. This advantageously allows an improved denoising performance.
• the processor is configured to extract the edges of the material inhomogeneities from the vector- valued image with a reduced noise level. This advantageously provides an improved image denoising with reduced and suppressed crosstalk.
• the processor is configured to extract the edges of the material inhomogeneities by applying a Sobel operator, a Prewitt operator, a Marr-Hildreth operator, a Laplacian operator or a differential edge detection to the vector- valued image. This advantageously allows an improved denoising performance.
• the processor is configured to extract the edges of the material inhomogeneities by applying a classification algorithm, like a support vector machine or neuronal network, on features extracted from the images. This advantageously allows an improved denoising performance.
• the processor is configured to apply the classification algorithm which gives a high value - higher than an average value or higher than an initially present value - in each pixel, if material inhomogeneities, like edges are most likely to be present. In other words, if edges are detected with a certain probability, for instance if there is a detection of an edge with the probability of 95 % that the detection is true. For pixel with high values, the covariance and thus the crosstalk are advantageously reduced by the processor applying the classification algorithm.
• a computer program performing the method of the present invention may be stored on a computer-readable medium.
• a computer-readable medium may be a floppy disk, a hard disk, a CD, a DVD, an USB (Universal Serial Bus) storage device, a RAM (Random Access Memory), a ROM (Read Only Memory) or an EPROM (Erasable Programmable Read Only Memory).
• a computer-readable medium may also be a data communication network, for example the Internet, which allows downloading a program code.
• DSP Digital Signal Processor
• ASIC application specific integrated circuit
• CPLD CPLD
• the present invention can be implemented in digital electronic circuitry or in computer hardware, firmware, software, or in combinations thereof, for instance in available hardware of conventional medical imaging devices or in new hardware dedicated for processing the methods described herein.
• Fig. 1 shows denoising results of a scatter image from a multi-channel photo/scatter reconstruction for explaining the present invention
• Fig. 2 shows denoising results of a scatter image from a multi-channel photo/scatter reconstruction in terms of a ground truth scatter image for explaining the present invention
• Fig. 3 shows a schematic photo effect images and Compton scatter images for explaining the present invention
• Fig. 4 shows a schematic diagram of a device for denoising a vector- valued image and a medical imaging system according to an exemplary embodiment of the present invention.
• Fig. 5 shows a schematic diagram of a flow-chart diagram for denoising a vector-valued image according to an exemplary embodiment of the present invention.
• Fig. 1 shows denoising results of a scatter image from a multi-channel photo/scatter reconstruction for explaining the present invention.
• images are split into different spatial frequency bands, e.g. high and low spatial frequencies. Depending on the frequency bands the correlation between the different materials is then modified in the cost function.
• the upper row shows the novel approach with a covariance set to zero in the low frequencies.
• the lower row shows a conventional denoising.
• the columns show different levels of regularization strength.
• the lower right image shows a large amount of cross-talk in the inserts, if compared with the ground truth as shown later in Fig. 2.
• the method for denoising a vector- valued image provides an improved approach which reduces this cross-talk, as shown in the upper right image of Fig. 1.
• the method for denoising vector-valued images allows to lower the correlation between the materials in the low- frequency bands and therefore reduce the crosstalk between the materials in these bands. This comes at the expense of a reduced performance of removing correlated noise in these bands as the noise model now assumes less correlation due to the reduced correlation.
• a tuning between cross-talk and correlated noise removal of low- frequency noise is provided by the processor and/or by the noise suppressor.
• Applying the method for denoising a vector- valued image provides an improved approach as shown in Fig. 1 and Fig. 2.
• Fig. 1 and Fig. 2 both show an example how the present method reduces the cross-talk.
• Fig. 2 shows denoising results of a scatter image from a multi-channel photo/scatter reconstruction in terms of a ground truth scatter image for explaining the present invention.
• ⁇ consist of all materials and pixel positions.
• the matrix Wean be viewed as a block-diagonal matrix with the inverted covariances of the original problem on the diagonal.
• ⁇ 0 ⁇ ⁇ 9 is a vector containing the different material values for each pixel of the input images, while ⁇ contains the material values of the denoised images for each pixel.
• W is the inverse noise variance in each pixel.
• R ( ⁇ ) is a regularization term and ⁇ a regularization strength parameter.
• the covariance matrix is constant for all pixel position across the image.
• the cost function can be reformulated to
• F LF and F HF are the spatial filters, which here operate on the different material images.
• the cost function obviously can be reduced to the original problem by choosing
• Fig. 3 shows a schematic photo effect images and Compton scatter images for explaining the present invention.
• Fig. 3 shows applications of the proposed method to simulated data.
• the upper row shows photo effect images, the lower row Compton scatter images.
• Fig. 3 from left to right, the following images are shown: i) Ground truth (phantom), ii) noisy input for denoising, iii) Denoising with original covariance matrices, iv) Denoising with modified covariance matrices according to the method for denoising of the present invention.
• root cause for the crosstalk between the material images is the representation of the strong noise correlation in the noise model. This becomes manifest in large negative values of the off- diagonal elements in the covariance-matrices C i . Furthermore, it can be observed that the crosstalk appears especially strongly at edges of inhomogeneities. Thus the idea is to reduce the absolute values of off-diagonal elements in the covariance-matrices C i at edges of inhomogeneities in the material images.
• the edges of inhomogeneities are extracted from an image with low noise level (e.g., by applying a Sobel operator to, for instance, a pre-denoised 70 keV mono-energy image), and to reduce the absolute values of the off-diagonal elements of those covariance-matrices that belong to image pixels with a strong edge response. Then, the statistical denoising is performed utilizing the modified covariance matrices. Results for this process are given in Fig. 3.
• Fig. 4 shows a schematic diagram of a device for denoising a vector- valued image according to an exemplary embodiment of the present invention.
• a medical imaging system 1000 may comprise a device 100 for denoising a vector- valued image.
• the medical imaging system 1000 may be for instance a computed tomography system, a C-arm based computed tomography, CT, system, an X-ray imaging system, a multispectral or spectral X-ray imaging system or a magnetic resonance imaging, MRI, system.
• the medical imaging system 1000 may be configured to provide vector- valued images in terms of multiple material images or in terms of multiple images of a scan.
• Medical imaging modalities such as MRI and CT scans produce large volumes of scalar or tensor
• a cost function is iteratively solved which has typically the form
• C i _1 is the inverse of the covariance matrix describing the noise between the values of the material images (e.g., photo effect and Compton scatter) for the same image pixel i. is a vector containing the different
• C i _1 is the inverse noise variance in each pixel.
• ⁇ a regularization strength parameter.
• the device According to an exemplary embodiment of the present invention, the device
• the 100 for denoising a vector- valued image may comprise a generator 10, a processor 20, and a noise-suppressor 30.
• the generator 10, the processor 20, and the noise-suppressor 30 may be an electronic device, or an electronic circuit configured to process the functions as described.
• the generator 10 is configured to generate an initial loss function L I comprising at least one initial covariance matrix ICM defining a model of correlated noise for each pixel of the vector- valued image.
• the processor 20 is configured to provide a final loss function L_F comprising a set of at least one final covariance matrix FCM based on the initial loss function by modifying at least one submatrix and/or at least one matrix element of the initial covariance matrix ICM.
• the noise-suppressor 30 is configured to denoise the vector-valued image using the final loss function L_F comprising the set of the at least one final covariance matrix FCM.
• Fig. 5 shows a schematic diagram of a flow-chart diagram denoising a vector- valued image according to an exemplary embodiment of the present invention.
• an initial loss function L I comprising at least one initial covariance matrix ICM defining a model of correlated noise for each pixel of the vector- valued image by means of a generator 10 may be performed.
• a final loss function L_F comprising a set of at least one final covariance matrix FCM based on the initial loss function L I by modifying at least one submatrix and/or at least one matrix element of the initial covariance matrix by means of a processor 20 may be performed.
• denoising S3 the vector-valued image using the final loss function L_F comprising the set of the at least one final covariance matrix FCM by means of a noise-suppressor 30 may be performed.
• the modifying of the at least one submatrix and/or of the at least one matrix element of the initial covariance matrix ICM for providing the final covariance matrix FCM is performed based on at least two different spatial frequency bands.
• the images are split into different spatial frequency bands, e.g. high and low spatial frequencies.
• the correlation between the different materials is then modified in the cost function at the expense of a reduced performance of removing correlated noise in these bands as the noise model now assumes less correlation due to the reduced correlation.
• the final loss function L_F comprising the final covariance matrix FCM based on the initial loss function L I is provided by reducing absolute values of off-diagonal elements of the initial covariance matrix ICM at edges of material inhomogeneities of the vector- valued image.
• the maximum likelihood function comprises a data term that models the noise statistics, commonly with a Gaussian noise model.
• this noise model is described by covariance matrices, which have a high correlation coefficient representing the strong noise correlation between the images. This strong correlation can lead to undesired cross-talk in the material image.
• the method presented here locally reduces the correlation to suppress the cross-talk in the material image.

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