1. A matrix transform system for coding images with weighted contribution of several points of the image to each points of the coded image and for decoding coded images with weighted contribution of several points of the coded image to each point of the decoded image, said system comprising: a. means for sampling the lines of an image to be coded and forming with said image samples a square matrix associated with the image; b. means for splitting said square matrix associated with the image into a plurality of first input component matrices of order 3N .times. 3N having a central part of order N .times. N ; c. means for multiplying each of said first input component matrices by a first rectangular coefficient matrix of order N .times. 3N having a square central part in which the coefficients are equal to positive or negative unity and two square lateral parts in which the coefficients are selectively equal to zero and .+-. .alpha. where .alpha. is a predetermined factor smaller than unity, and forming first intermediate matrices of order N .times. 3 d. means for multiplying each of said first intermediate matrices by a second rectangular coefficient matrix of order 3N .times. N which is the transpose of said first rectangular coefficient matrix, and forming first output matrices of order N .times. N, each of said first output matrices being the transform of the central part of a first input component matrix; e. means for forming with said first output matrices a square matrix associated with the coded image; f. means for splitting said square matrix associated with the coded image into a plurality of second input component matrices of order 3N .times. 3N having a central part of order N .times. N; g. means for multiplying each of said second input component matrices by a third rectangular coefficient matrix of order N .times. 3N having a square central part in which the coefficients are equal to positive or negative unity and two square lateral parts in which the coefficients are selectively equal to zero and (a) .+-. .alpha. where .alpha. is said predetermined factor smaller than unity and forming second intermediate matrices of order N .times. 3N; h. means for multiplying each of said second intermediate matrices by a fourth rectangular coefficient matrix of order 3N .times. N which is the transpose of said third rectangular coefficient matrix and forming second output matrices of order N .times. N, each of said second output matrices being the transform of the central part of a second input component matrix; and i. means for forming with said second output matrices a square matrix associated with the decoded image.