The Study On Some Key Problems Of Quantum Image Processing

Quantum image processing(QIP)is a new crossover research direction which studies ways to represent and operate an image on quantum computers.It presents a different methodology and a novel angle of view to image processing,and also brings a potential direction for the ap-plication of quantum computation.So far,research achievements have already shown the great superiority and broad prospect of this direction.However,as a whole,QIP is still in its infancy.It lacks effective means of image transformation and analysis,lacks effective implementation methods of complicated operations such as compression,recognition,and brings some new problems when infusing quantum properties.All these troubles have restricted further development of this direction.Based on the anal-ysis of the current research status,we choose the two key issues as the entry points to break through the restriction.One is quantum image features extraction method,which is the foun-dation of some complicated image operations such as recognition,compression;the other is quantum image retrieval and classification,which are suitable for quantum computing,and will.adequately exert the advantages of quantum computation.Specifically,our contributions in-volved in these two aspects include:(1)quantum image feature extraction methodImage features extraction and expression methods provide data support for retrieval algo-rithm and recognition algorithm,play a vital role for the correct implementation of the algo-rithm.We studied the classical PCA,re-expressed classic image features as quantum superpo-sition state,and used Grover algorithm to accelerate the recognition process of human faces.Besides,we found the features extraction method on quantum image directly.Global features of quantum image could be defined as Schmidt coefficients with big values after performing Schmidt decomposition on quantum image.The experiments demonstrate the rationality and the validity of this method.Before this work,there are few works involved in quantum image feature extraction method.This work laid a good foundation for subsequent research.(2)quantum image retrievalQuantum image retrieval is a compulsory process for obtaining quantum image manipu-lation results.In quantum image processing context,the nature of this operation is quantum state tomography,which is a time-exhaustive operation with exponential measurement scales.Based on the achievement of(1),we did block cutting on the quantum image,prepared each block as a quantum state,executed Schmidt decomposition on it,selected large values of the decomposed coefficients,and then mapped these coefficients to permutation invariant states by base transformation,finally with the help of Toth's method,reduced the measurement scales to square level.This method offered an effective solution for the quantum image retrieval.(3)the quantum image classificationIn quantum image processing scenarios,image retrieval and image classification are both required to perform measurements to get information,but in general,classification does not need to perform perfect tomography to reconstruct quantum image,provided that partial information gotten are sufficient to classify a target to a correct category by certain similarity measurement.Schuld's algorithm is a classification algorithm based on computing Hamming distance.We found that the efficiency of the algorithm becomes very low with the big tomographic cost as the classification categories growing.We distinguished the right category index from others by setting an appropriate threshold,as a result,avoided doing tomography to obtain the final classification result,greatly improved the efficiency of the algorithm.All in all,aiming at quantum image features extraction method and the retrieval and recog-nition methods of quantum images,we put forward our own solutions and ideas,enriched and developed this research direction.