Research On Optimizing Of Measurement Method In Compressed Sensing

Compressed Sensing theory is a new codec method which was proposed in recent years. Itbreaks the Nyquist sampling theorem constraints. Compared to the traditional codec theory, thegreatest advantage of compressed sensing codec theory is its encoding process is extremely simple,the complexity is transferred to the decoding side, which has its unique advantages in strongmobility, limited computing power and lower storage capacity occasion. But compared to thetraditional codec theory, signal reconstruction quality of compressed sensing codec method remainsto be improved. The main purpose of this paper is to optimize the coding method of compressedsensing, including optimization of the measurement matrix, adaptive selection of measurements,measurements quantization method.As the coding method of compressed sensing is a projection process of the signal onto ameasurement matrix, the quality of measurement matrix directly affects the codec quality, so thepaper starts from optimizing of the measurement matrix, Two measurement matrix optimizationalgorithms is proposed: one is the upper triangular weighted measurement matrix optimizationalgorithm, which can enhance the sampling of low frequency coefficients; the other is thegradient-based Gram matrix iterative optimization, which can reduce the relevance of measurementmatrix and sparse matrix. Experiments show that these two optimizations can improve theperformance of existing measurement matrix.Secondly, a maximum posteriori variance based adaptive selection of measurements algorithmis proposed, which is mainly about "For a known measurement matrix, selecting which lines can getthe best measurements" and "Selecting how many lines are adequate for the current signal".According to this algorithm, a measurement matrix which has large number rows is selected first,then selecting the right rows according to this algorithm. Experimental results show that theproposed adaptive algorithm can get better reconstruction quality compared to the conventionalmeasurement method at the same conditions.Finally, research about the quantization of compressed sensing measurements is done in thispaper. Works about quantization of measurements is not too much, but in practical applications,quantization must be considered. As the theory of compressed sensing indicates that eachmeasurement is equally important, compressed sensing measurements are commonly uniformquantized. A statistics is made from a large number of measurements, which finds that the compressed sensing measurements obtained by the Gaussian random matrices are approximateGaussian distribution. According to this distribution characteristic, a Gaussian quantization methodis proposed, the main idea is to quantize the measurements whose magtitude are large finely andquantize the measurements whose magtitude are small coarsely. When applied to video codec, theproposed quantization method is better than the current commonly used uniform quantization.