Cross Low-Dimension Pursuit for Sparse Signal Recovery from Incomplete Measurements Based on Permuted Block Diagonal Matrix

نویسندگان

  • Zaixing He
  • Takahiro Ogawa
  • Miki Haseyama
چکیده

In this paper, a novel algorithm, Cross Low-dimension Pursuit, based on a new structured sparse matrix, Permuted Block Diagonal (PBD) matrix, is proposed in order to recover sparse signals from incomplete linear measurements. The main idea of the proposed method is using the PBD matrix to convert a high-dimension sparse recovery problem into two (or more) groups of highly low-dimension problems and crossly recover the entries of the original signal from them in an iterative way. By sampling a sufficiently sparse signal with a PBD matrix, the proposed algorithm can recover it efficiently. It has the following advantages over conventional algorithms: (1) low complexity, i.e., the algorithm has linear complexity, which is much lower than that of existing algorithms including greedy algorithms such as Orthogonal Matching Pursuit and (2) high recovery ability, i.e., the proposed algorithm can recover much less sparse signals than even 1-norm minimization algorithms. Moreover, we demonstrate both theoretically and empirically that the proposed algorithm can reliably recover a sparse signal from highly incomplete measurements. key words: sparse recovery, sparsest solution, compressed sensing, permuted block diagonal matrix, greedy algorithms, orthogonal matching pursuit, 1-norm minimization, basis pursuit

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Block-Wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...

متن کامل

A Compressed Sensing-Based Low-Density Parity-Check Real-Number Code

In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing. A real-valued message is encoded by a coding matrix (with more rows than columns) and transmitted over an erroneous channel, where sparse errors (impulsive noise) corrupt the codeword. In the decoding procedure, we apply a structured sparse (low-density) parity-check matrix, the Permuted Bl...

متن کامل

Signal Recovery from Inaccurate and Incomplete Measurements via Regularized Orthogonal Matching Pursuit

We demonstrate a simple greedy algorithm that can reliably recover a vector v ∈ R from incomplete and inaccurate measurements x = Φv + e. Here Φ is a N × d measurement matrix with N ≪ d, and e is an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to close the gap between two major approaches to sparse recovery. It combines the speed and ease of implementation ...

متن کامل

Greedy signal recovery and uncertainty principles

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of t...

متن کامل

Stochastic Recovery Of Sparse Signals From Random Measurements

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal recovery problem is based on the basis pursuit method. This approach requires the solution of a large convex optimization problem, and therefore suffers from h...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • IEICE Transactions

دوره 94-A  شماره 

صفحات  -

تاریخ انتشار 2011