Blind reconstructing method of block sparse signal with unknown block size
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A block sparse, block size technology, applied in the field of block sparse signal reconstruction, can solve the problems of high complexity, difficult to obtain, over-matching, etc., to achieve the effect of blind reconstruction
Inactive Publication Date: 2012-12-26
HARBIN INST OF TECH
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The L-POT algorithm is a norm-based algorithm. It uses convex optimization to solve the problem. The complexity is high. The BMP algorithm and the BOMP algorithm are greedy algorithms. Once these two algorithms find a matching atom, they will not change, so it is easy to cause over-matching. , and these algorithms all require block size d or block sparsity K etc. as prior knowledge, which is difficult to obtain in practice
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specific Embodiment approach 1
[0023] Specific implementation mode one : the blind reconstruction method of the block sparse signal of unknown block size of the present embodiment, its specific process is as follows:
[0024] Step 1. Obtain block sparse signal x observation signal y ,and y ;make Φ represents the measurement matrix, and ; Initialize block sparsity k , the initial block size d , initialize the residual r 0 = y , initialize the recovery matrix , the initial step size step =1, initialize the signal support set size S = k , the number of initialization iterations l =1;
[0025] Step 2. According to the block size d , will measure the matrix Φ Divided into M block, use Indicates the first i sub-block;
[0026] Step three, order , i =1,2,..., M ;
[0027] The meaning of this formula is: first obtain and multiplied by , to get a The vector of this vector N The elements are divided into blocks according to the block method of the block vector M block, then fin...
specific Embodiment approach 2
[0041] Specific implementation mode two: This embodiment is a further description of the blind reconstruction method of the block sparse signal whose block size is unknown in Embodiment 1. The block sparsity described in step 1 k The initialized range is ,in K is the true block sparsity of the source signal.
specific Embodiment approach 3
[0042] Specific implementation mode three: This embodiment is a further description of the blind reconstruction method of the block sparse signal whose block size is unknown in the second embodiment, the block sparsity k Initialized to 1.
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Abstract
The invention relates to a blind reconstructing method of a block sparse signal with unknown block size, relating to the technical field of compressed sensing and solving the problem that the traditional reconstructing method of the block sparse signal needs take the block size and block sparsity as priori knowledge. The blind reconstructing method comprises the following steps of: carrying out block sparsity self-adaptation iteration of an algorithm for each block size to find a reconstructed signal which corresponds to each block size by initializing the block sparsity and the block size; continuously iterate the algorithm and enlarging the block size accordingly, and finishing the algorithm till the 0-norm of the reconstructed signal obtained through the algorithm is less than the line number of a measurement matrix, outputting the reconstructed signal used as algorithm; if the condition is not met, operating the algorithm till: when block size is smaller than or equal to haft of the length of the reconstructed signal, the product of the block size and the block sparsity is larger than or equal to the length of the reconstructed signal, the iteration is completed, and a series of reconstructed signals are obtained; and finally screening the sparsest reconstructed signal as final algorithm output by utilizing 0-norm sparsity measurement criteria. The invention can be used for the technical field of compressed sensing of the block sparse signal.
Description
technical field [0001] The invention relates to the technical field of compressed sensing, in particular to a method for reconstructing 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...
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