Denoising of dynamic magnetic resonance spectroscopic imaging using low rank approximations in the kinetic domain

Abstract

Kinetic monitoring of in vivo metabolism of labelled tracers is based on singular value decomposition or Tucker Decomposition of magnetic resonance spectral image data. Data decomposition is used in conjunction with rank reduction to improve signal-to-noise ratio. Rank reduction can be applied in one or more of a spectral, spatial, or temporal dimension. Rank is generally reduced based on a number of expected analytes/metabolites or fit of measured data to a model.

1 . A method, comprising:
 in a magnetic resonance imaging system:
 acquiring a magnetic resonance imaging signal associated with a plurality of chemical shifts for at least one voxel at a plurality of times; 
 arranging the magnetic resonance imaging signal as a data matrix; 
 obtaining a singular value decomposition of the data matrix; 
 rank reducing the singular value decomposition; and 
 obtaining a rank-reduced data matrix based on the rank-reduced singular value decomposition. 
   
     
     
         2 . The method of  claim 1 , further comprising rank reducing the singular value decomposition based on a number of analytes. 
     
     
         3 . The method of  claim 2 , further comprising injecting a tracer so that the acquired magnetic resonance imaging signal is associated with metabolism of the tracer, wherein the analytes include the tracer or one more metabolic products associated with the tracer. 
     
     
         4 . The method of  claim 3 , wherein the number of analytes corresponds to a number of metabolic products. 
     
     
         5 . The method of  claim 1 , wherein the data matrix is an m×n data matrix, m is an integer number of measurement times and n is an integer number of measured chemical shifts and the singular value decomposition includes matrices U, Σ, V T , wherein U is an m×m unitary matrix, Σ is a diagonal m×n matrix with non-negative real numbers on the diagonal, and V T  is an n×n orthogonal matrix. 
     
     
         6 . The method of  claim 5 , wherein rank reduction includes setting r smallest diagonal values of the matrix Σ to zero to form a matrix Σ′, wherein the rank-reduced data matrix is obtained as a matrix product U·Σ′·V T . 
     
     
         7 . The method of  claim 6 , wherein the diagonal values of the matrices Σ and Σ′ are arranged in rows of the matrices from largest to smallest. 
     
     
         8 . The method of  claim 1 , wherein the magnetic resonance imaging signal is associated with the plurality of chemical shifts for the plurality of voxels at the plurality of times, and for each voxel, the magnetic resonance imaging signal is arranged as a data matrix, a singular value decomposition of the data matrix is obtained that is then rank reduced, and rank reduced data matrices are produced for each of the plurality of voxels. 
     
     
         9 . A magnetic resonance imaging apparatus, comprising:
 a magnet situated to establish an axial magnetic field in a specimen;   a plurality of coils situated to apply electromagnetic pulse sequences to the specimen;   a receiver situated to detect electromagnetic signals from the specimen in response to the applied electromagnetic pulse sequences; and   a controller coupled to the plurality of coils so as to selectively apply the electromagnetic pulse sequences and to the receiver to store signal values associated with the detected signals for a plurality of specimen voxels, and process the detected signal by rank reducing a singular value decomposition associated with a matrix representation associated with at least one of the plurality of specimen voxels.   
     
     
         10 . The magnetic resonance imaging apparatus of  claim 9 , wherein the controller processes the detected signals by rank reducing singular value decompositions associated with matrix representations associated with each the plurality of specimen voxels. 
     
     
         11 . The magnetic resonance imaging apparatus of  claim 10 , wherein the rank reduction of the singular value decomposition is based on a number of analytes. 
     
     
         12 . The magnetic resonance imaging apparatus of  claim 11 , further comprising an injector situated to inject a tracer into the specimen, the injector coupled to the controller so that the detected electromagnetic signals are associated with metabolism of the injected tracer, wherein the analytes include the tracer or one more metabolic products associated with the tracer. 
     
     
         13 . The magnetic resonance imaging apparatus of  claim 12 , wherein the number of analytes corresponds to a number of metabolic products. 
     
     
         14 . The magnetic resonance imaging apparatus of  claim 13 , wherein the matrix representation for each voxel is an m×n data matrix, wherein m is an integer number of measurement times and n is an integer number of measured chemical shifts and the singular value decomposition includes matrices U, Σ, V T , wherein U is an m×m unitary matrix, Σ is a diagonal m×n matrix with non-negative real numbers on the diagonal, and V T  is an n×n orthogonal matrix. 
     
     
         15 . The magnetic resonance imaging apparatus of  claim 14 , wherein rank reduction includes setting r smallest diagonal values of the matrices Σ to zero to form matrices Σ′, wherein the rank-reduced data matrices are obtained as matrix products U·E′·V T . 
     
     
         16 . The magnetic resonance imaging apparatus of  claim 15 , wherein the diagonal values of the matrices Σ and Σ′ are arranged in rows of the matrices from largest to smallest. 
     
     
         17 . The magnetic resonance imaging apparatus of  claim 16 , wherein the magnetic resonance imaging signal is associated with the plurality of chemical shifts for the plurality of voxels at the plurality of times, and for each voxel, the magnetic resonance imaging signal is arranged as a data matrix, a singular value decomposition of the data matrix is obtained that is then rank reduced, and rank reduced data matrices are produced for each of the plurality of voxels. 
     
     
         18 . The magnetic resonance imaging apparatus of  claim 17 , further comprising displaying an image using the rank reduced data matrices. 
     
     
         19 . A method, comprising:
 in a magnetic resonance imaging system:
 acquiring a magnetic resonance imaging signal associated with a plurality of chemical shifts for a plurality of voxels at a plurality of times; 
 arranging the magnetic resonance imaging signal as a data tensor; 
 obtaining a Tucker decomposition of the data tensor; and 
 spatially or temporally rank reducing the Tucker decomposition to produce spatially or temporally denoised voxel data for each of the plurality of voxels. 
   
     
     
         20 . The method of  claim 19 , wherein the rank reduction is temporal rank reduction. 
     
     
         21 . The method of  claim 20 , further comprising injecting a tracer so that the acquired magnetic resonance imaging signal is associated with metabolism of the tracer, wherein the analytes include the tracer or one more metabolic products associated with the tracer. 
     
     
         22 . The method of  claim 21 , wherein the rank reduction is spectral rank reduction based on a number of metabolic products. 
     
     
         23 . The method of  claim 19 , wherein the rank reduction is based on differences between measured data and truncated model data. 
     
     
         24 . The method of  claim 19 , wherein Tucker Decomposition includes a core tensor and a plurality of orthogonal factor matrices. 
     
     
         25 . The method of  claim 1 , wherein the data tensor includes data matrices for each of the plurality of voxels, wherein the data matrices are m×n data matrices, wherein m is an integer number of measurement times and n is an integer number of measured chemical shifts. 
     
     
         26 . A method, comprising:
 in a magnetic resonance imaging system:
 acquiring magnetic resonance imaging signals for a plurality of voxels as a function of at least two parameters; 
 arranging the magnetic resonance imaging signals as a data tensor; 
 obtaining a Tucker decomposition of the data tensor; and 
 rank reducing the Tucker decomposition to produce processed voxel data for each of the plurality of voxels based on at least one of the two parameters; and 
   
     
     
         27 . The method of  claim 26 , wherein the processed voxel data is represented as data matrices for each of the voxels. 
     
     
         28 . The method of  claim 27 , wherein the rank reducing the Tucker decomposition to produce processed voxel data for each of the plurality of voxels based both of the at least two parameters. 
     
     
         29 . The method of  claim 28 , wherein the processed voxel data is denoised voxel data.