Minimax risk of matrix denoising by singular value thresholding
نویسندگان
چکیده
منابع مشابه
Minimax Risk of Matrix Denoising by Singular Value Thresholding
An unknown m by n matrix X0 is to be estimated from noisy measurements Y = X0 + Z, where the noise matrix Z has i.i.d Gaussian entries. A popular matrix denoising scheme solves the nuclear norm penalization problem minX‖Y − X‖F /2 + λ‖X‖∗, where ‖X‖∗ denotes the nuclear norm (sum of singular values). This is the analog, for matrices, of `1 penalization in the vector case. It has been empiricall...
متن کاملDenoising time-resolved microscopy image sequences with singular value thresholding.
Time-resolved imaging in microscopy is important for the direct observation of a range of dynamic processes in both the physical and life sciences. However, the image sequences are often corrupted by noise, either as a result of high frame rates or a need to limit the radiation dose received by the sample. Here we exploit both spatial and temporal correlations using low-rank matrix recovery met...
متن کاملDenoising PET Images Using Singular Value Thresholding and Stein's Unbiased Risk Estimate
Image denoising is an important pre-processing step for accurately quantifying functional morphology and measuring activities of the tissues using PET images. Unlike structural imaging modalities, PET images have two difficulties: (1) the Gaussian noise model does not necessarily fit into PET imaging because the exact nature of noise propagation in PET imaging is not well known, and (2) PET ima...
متن کاملGeneralized Singular Value Thresholding
This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑
متن کاملGeneralized Singular Value Thresholding
This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2014
ISSN: 0090-5364
DOI: 10.1214/14-aos1257