论文标题
关于CP等级较低的随机压缩张量的可恢复性
On Recoverability of Randomly Compressed Tensors with Low CP Rank
论文作者
论文摘要
我们的兴趣在于\ textIt {canonical polyadic分解}（CPD）模型下压缩张量的可回收性属性。在许多应用中，例如高光谱图像和视频压缩，被认为的问题激励了。先前的工作在某种特殊的假设下研究了这个问题 - 例如，张量的潜在因素是稀疏或从绝对连续的分布中得出的。我们提供了另一种结果：我们表明，如果张张器通过次高斯线性映射压缩，则如果测量次数的数量与模型参数的数量级相同，则可以恢复张量，而没有对潜在因子没有强有力的假设。我们的证明是基于通过集合覆盖技术在CPD模型下得出\ textit {限制的等轴测属性}（r.i.p。），从而表现出经典压缩感的味道。新的可恢复性结果丰富了对压缩的CP张量恢复问题的理解；它为恢复元素不一定是连续或稀疏的张量提供了理论保证。
Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video compression. Prior work studied this problem under somewhat special assumptions---e.g., the latent factors of the tensor are sparse or drawn from absolutely continuous distributions. We offer an alternative result: We show that if the tensor is compressed by a subgaussian linear mapping, then the tensor is recoverable if the number of measurements is on the same order of magnitude as that of the model parameters---without strong assumptions on the latent factors. Our proof is based on deriving a \textit{restricted isometry property} (R.I.P.) under the CPD model via set covering techniques, and thus exhibits a flavor of classic compressive sensing. The new recoverability result enriches the understanding to the compressed CP tensor recovery problem; it offers theoretical guarantees for recovering tensors whose elements are not necessarily continuous or sparse.
