一种自适应低采样率图像分块压缩感知算法

An Adaptive Reconstruction Algorithm for Image Block Compressed Sensing Under Low Sampling Rate

分块压缩感知(BCS)适用于图像信号的压缩感知(CS)处理.当采样率较低时,BCS迭代阈值投影(BCS-SPL)算法对图像纹理部分重构质量差,针对此不足,提出基于全变差分自适应采样率BCS正交匹配追踪(Total Variation based Sampling Adaptive Block Compressed Sensing w ith OM P,TVSA-BCS-OM P)算法,该算法对图像重叠分块以消除重构结果的块效应,根据图像子块的纹理复杂度自适应分配采样率,并且子块的纹理复杂度用各自的全变差分进行测量,从而全变差分较大的子块可获得更高采样率.各子块由纹理分配采样率保留变换域下的非零系数,分别进行CS采样以及OMP重构.实验结果显示,当图像初始采样率较低(低于0.2)时,TVSA-BCS-OMP算法的重构精度始终高于BCS-SPL算法,特别是对图像纹理块的重构质量更高,并且前者的重构时间比后者更低.

Block Compressed Sensing（ CS） adapts to compressed sensing for an image. As the famous BCS with Smoothed Projected Landweber algorithm（ BCS-SPL） shows bad performance when the sampling rate is in a lowcondition,we propose a novel algorithm called Total Variation based Sampling Adaptive Block Compressed Sensing with OMP（ TVSA-BCS-OMP） to solve the following problem of BCS-SPL. TVSA-BCS-OMP blocks the whole image in an overlapping way to eliminate blocking effect. It assigns sampling rate depending on each block＇ texture complexity,which is measured by the block＇s Total Variation（ TV） so that the blocks with big TV can attain higher sampling rate. Then only limited nonzero coefficients in each block are retained according to the adaptively assigned sampling rate. At last,we sample the blocks and conducts OMP reconstruction respectively. The experimental results showthat under the condition of lowinitial sampling rate（ lower than 0. 2）,TVSA-BCS-OMP shows better reconstruction precision,especially can attain better reconstruction performance in the texture blocks than BCS-SPL. In addition,the newalgorithm costs shorter reconstruction time than BCS-SPL algorithm.