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Compressed sensing reconstructing method of sparse signal with unknown block sparsity

A technology for compressive sensing reconstruction and sparse signal, applied in the field of compressive sensing, which can solve the problem of inability to reconstruct

Inactive Publication Date: 2010-12-08
HARBIN INST OF TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] In order to solve the over-matching phenomenon in the existing block sparse signal matching tracking reconstruction method, and the unknown block sparsity K The problem that cannot be reconstructed when the block sparsity is unknown, a sparse signal compression sensing reconstruction method with unknown block sparsity is proposed

Method used

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  • Compressed sensing reconstructing method of sparse signal with unknown block sparsity
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  • Compressed sensing reconstructing method of sparse signal with unknown block sparsity

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specific Embodiment approach 1

[0032] Specific implementation mode one, to combine figure 1Describe this embodiment, a sparse signal compression sensing reconstruction method with unknown block sparsity, the specific process is as follows:

[0033] Acquire the source signal x The observed signal is y , the observed signal y Expressed as y T =[ y 1 , y 2 , y 3 ..., y m ],in m for the observed signal y length,

[0034] Step 1. Sparse signal compression sensing reconstruction process initialization: set the initialization block sparsity k , , K source signal x The block sparsity of , initialize the measurement matrix , set the iteration error err, block vector Group , a block vector Group Expressed as follows:

[0035]

[0036] in, d is a block vector Group The length of the sub-block, set the initial value of the residual r 0 = y , restore the matrix , the step size step =1, signal support set size S = k , the source signal x The reconstruction vector of ;

[0...

specific Embodiment approach 2

[0067] Specific implementation mode two, This implementation mode is a further description of the specific implementation mode 1. In step 1, the block sparsity is initialized k= 1. Iteration error err=10 -5 , the measurement matrix follow a Gaussian distribution.

specific Embodiment approach 3

[0068] Specific implementation mode three, This embodiment is a further description of the second specific embodiment, the measurement matrix ,in , is the measurement matrix The normalized column vector of , , is the column vector of the original measurement matrix, Represents the 2-norm.

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Abstract

The invention relates to a compressed sensing reconstructing method of a sparse signal with the unknown block sparsity, belonging to the technical field of compressed sensing, in particular to a reconstruction method of a block sparse signal. The method comprises the steps of finding out one subset of a signal support set by initializing block sparsity k and iterating each block sparse signal, increasing the block sparsity while keeping iteration and finally finding out the support set of the whole source signal x so as to achieve the purpose of reconstructing the source signal x. The invention has high reconstruction precision by iterating and modifying the support set many times, and has high probability for reconstructing block sparse signals without the overmatching phenomenon compared with the traditional block sparsity matching and tracking and orthogonal matching and tracking method. The invention does not need the block sparsity as the priori knowledge and is particularly suitable for the reconstruction field of signals with unknown block sparsity.

Description

technical field [0001] The invention relates to the technical field of compressed sensing, in particular to a reconstruction method for block sparse signals. Background technique [0002] The traditional signal sampling theory is based on the Nyquist sampling theorem, that is, in order to ensure that the information of the source signal is not lost and to restore the source signal without distortion, the sampling rate needs to be at least twice the signal bandwidth. This often requires a high sampling rate for the digitization of broadband analog signals, which increases the burden on physical devices. And for signals with a large amount of data, the storage capacity and processing speed are further limited. [0003] Compressed Sensing (CS) is a brand-new signal sampling theory proposed in 2004. Its idea is to observe the signal globally at a speed much lower than the Nyquist sampling rate for sparse signals, and then pass appropriate re- The construction algorithm reconst...

Claims

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Application Information

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IPC IPC(8): H03M7/30
Inventor 付宁乔立岩马云彤曹离然彭喜元
Owner HARBIN INST OF TECH
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