On the Nuclear Norm heuristic for a Hankel matrix Recovery Problem
نویسندگان
چکیده
This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable singlereal-pole system, if elements of the upper-triangle of the associated Hankel matrix are given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply in the considered situation. A ’certificate’ which guarantees the success of the matrix completion task is constructed by exploring the structural information of the hidden matrix. Experimental results and discussions regarding the nuclear norm heuristic applied to a more general setting are also given.
منابع مشابه
On some sparsity related problems and the randomized Kaczmarz algo- rithm
This thesis studies several problems related to recovery and estimation. Specifically, these problems are about sparsity and low-rankness, and the randomized Kaczmarz algorithm. This thesis includes four papers referred to as Paper I, Paper II, Paper III, and Paper IV. Paper I considers how to make use of the fact that the solution to an overdetermined system is sparse. This paper presents a th...
متن کاملNecessary and Sufficient Null Space Condition for Nuclear Norm Minimization in Low-Rank Matrix Recovery
Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem is an NP hard problem and thus challenging. A commonly used heuristic approach is the nuclear norm minimization. In [12,14,15], the authors established the ne...
متن کاملSeparation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach
We consider the problem of recovering the superposition of R distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the R frequencies or the missing data. However, it is known that in order for TV minimization and atomic norm minimization to recover the missin...
متن کاملSubspace identification with missing data
The paper presents initial results on a subspace method for exact identification of a linear time-invariant system from data with missing values. The identification problem with missing data is equivalent to a Hankel structured lowrank matrix completion problem. The novel idea is to search systematically and use effectively completely specified submatrices of the incomplete Hankel matrix constr...
متن کاملSpectral Compressed Sensing via Structured Matrix Completion
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension n is assumed to be a mixture of r complex multi-dimensional sinusoids, while the underlying frequencies can assume any value in the unit disk. Conventional compressed sensing paradigms suffer from the basis mismatch issue ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1207.4420 شماره
صفحات -
تاریخ انتشار 2012