A Sparse Representation Image Denoising Method Based on Orthogonal Matching Pursuit

Image denoising is an important research aspect in the field of digital image processing, and sparse representation theory is also one of the research focuses in recent years. The sparse representation of the image can better extract the nature of the image, and use a way as concise as possible to express the image. In image denoising based on sparse representation, the useful information of the image possess certain structural features, which match the atom structure. However, noise does not possess such property, therefore, sparse representation can effectively separate the useful information from noise to achieve the purpose of denoising. Aiming at image denoising problem of low signal-to-noise ratio (SNR) image, combined with Orthogonal Matching Pursuit and sparse representation theory, this paper puts forward an image denoising method. The experiment shows that compared with the traditional image denoising based on Symlets, image denoising based on Contourlet transform, this method can delete noise in low SNR image and keep the useful information in the original image more efficiently

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture

We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type