Imaging Through Scattering Media Based On Transmission Channel Theory

Different from homogeneous media and inhomogeneous media,the distribution of scatterers inside random media(also named scattering media)is always unknown,and each scatter behaves different from others,which means the refractive indexes are not the same everywhere.In that case,light inside random media would be scratched once or more times,could not travel in a straight line,phase would be randomized to varying degrees,scattered lights interfere with each other,thus we can only image a speckle pattern rather than the target object hidden behind the random media.Imaging through scattering media is the technique which helps image objects hidden behind random media,when random media is present.Typical algorithms for imaging through random media include phase conjugation based adaptive wavefront feed-back modulation algorithm,transmission matrix(TM)based algorithm,phase-retrieval based algorithm and machine learning based algorithm,but there is some deficiencies on each of them: i)utilizing adaptive wavefront feed-back modulation algorithm for focusing is always complex and time-consuming,and a reference known object is always needed for imaging which is almost impossible in real applications;ii)TM based algorithm can be divided into two parts according to the TM measurement style,one is using a separate unscattered light path to interfere with the scattered one to obtain the TM,the other is self-referenced setup(i.e.for a square object plane,the light outside light beam can be viewed as reference light while the light beam serves as scattered light).The former requires strict light path calibration and the whole system would be relatively complex,while the latter’s system is relatively simple but the measurement is not strictly accurate in theoretical;iii)phase-retrieval based algorithm is much efficient but could not access accurate phase of target due to the limitation of phase-retrieval algorithm itself;iv)machine learning based algorithm is also limited by the feature driven character of machine learning algorithms.Aimed at the deficiencies mentioned above,contributions of this paper are listed as follows:First,as for the not satisfying efficiency,this paper validates image reconstruction performance using TM based algorithm whose TM is measured with self-referenced setup and phase-retrieval based algorithm separately.Based on existing TM based algorithm,this paper proposes using semidefinite programming(SDP)for imaging through scattering media.In detail,for a scattering system,the proposed algorithm first measures the TM of scattering media,and then lift the input object images and their corresponding output speckle patterns to their autocorrelation space respectively,obtain the product of the unknown object image and its Hermitian transposition by solving a SDP problem,then image of the target object could be reconstructed by extracting the largest rank-1 component of the product.Relevant experiments validates that the proposed algorithm is effective and efficiency,and high reconstruction fidelity could be achieved especially for sparse object images.Second,this paper validates the limitation when simply using support vector regression(SVR)based algorithm for imaging through scattering media.To be exact,when only one class of input object images and their output speckle patterns are grouped and used to train the inverse scattering function(ISF)of a scattering system,the learned ISF would be only effective for the exact same class of speckle pattern and scattered object image could be reconstructed,but the ISF would fail when facing speckle patterns of objects in other classes.Meanwhile,this paper compares the image reconstruction performance when different kernel function is used,and ISFs trained with different number of training pairs are also tested,finally the conclusion that the image reconstruction limitation maybe caused by the feature driven character of machine learning based algorithms is drawn.Third,this paper lifts the input object object images and their output speckle patterns to their autocorrelation space respectively,and proves the two own the same singular value distribution after rigorous formula derivation.Thus,this papers proposes when scattering media is present,scattered object recognition can be replaced with speckle recognition,bypassing the conventional object reconstruction procedure.In general,simply using a group of known speckle patterns(label shared from their corresponding object images)to train a classifier,then applying the classifier to unlabeled speckle pattern,finally the class of the target object could be accessed.Relevant experiments validates the effectiveness and practicality of the proposed method.Forth,based on the analysis above,this paper combines the same singular value distribution conclusion and the limitation when simply using support vector regression for imaging through scattering media mentioned above,and proposes speckle pattern classification based support vector regression method for imaging through scattering media.That is,for an unknown object,once its speckle pattern is measured,a classifier learned previously could be applied to recognize its class character,and the ISF of the exact class could be selected and utilized for the unknown object image regression or reconstruction.The effectiveness of the proposed method has been validated through relevant experiments.