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Deep learning, particularly the generative model, has demonstrated tremendouspotential to significantly speed up image reconstruction with reducedmeasurements recently. Rather than the existing generative models that oftenoptimize the density priors, in this work, by taking advantage of the denoisingscore matching, homotopic gradients of generative density priors (HGGDP) areproposed for magnetic resonance imaging (MRI) reconstruction. More precisely,to tackle the low-dimensional manifold and low data density region issues ingenerative density prior, we estimate the target gradients inhigher-dimensional space. We train a more powerful noise conditional scorenetwork by forming high-dimensional tensor as the network input at the trainingphase. More artificial noise is also injected in the embedding space. At thereconstruction stage, a homotopy method is employed to pursue the densityprior, such as to boost the reconstruction performance. Experiment resultsimply the remarkable performance of HGGDP in terms of high reconstructionaccuracy; only 10% of the k-space data can still generate images of highquality as effectively as standard MRI reconstruction with the fully sampleddata.

Homotopic Gradients of Generative Density Priors for MR Image Reconstruction