A method of acquiring high-resolution ultrasound images of a medium using an array of N transducers (T1 to TN) using successive transmission matrices, characterized in that it comprises the steps of: a) acquiring at least one preliminary image of the medium; b) defining an area of interest in the preliminary image; c) determining inter-transducer correlation matrices corresponding to the area of interest and to an unwanted area the unwanted area being the rest of the half-space in front of the probe; d) determining a characteristic matrix of the area of interest resulting from the product of the inverse of the inter-transducer correlation matrix of the unwanted area by the inter-transducer correlation matrix of the area of interest; e) calculating eigenvectors and eigenvalues of the characteristic matrix of the area of interest, these vectors, classified as a function of their corresponding eigenvalues, defining a transmission matrix; f) selecting the K eigenvectors associated with the K highest eigenvalues; g) firing K waves weighted by the selected K eigenvectors, each selected vector weighting the signals transmitted by the transducers (T1 to TN) during a firing, these vectors defining a truncated transmission matrix composed of, in a first part, the K vectors of the family of eigenvectors associated with the K highest eigenvalues of the characteristic matrix and, in a second part, columns of zeros corresponding to the firings that are not effected; h) receiving the signals returned by the medium; i) multiplying a reception matrix constituted of the acquired signals completed by data set to zero corresponding to the firings not effected by the inverse of the transmission matrix to obtain a complete data set; j) extracting low-resolution images from the complete data set as in synthetic aperture echographic imaging methods; and k) reconstructing the high-resolution image corresponding to the area of interest by coherent summing, as in synthetic aperture echographic imaging methods, of the low-resolution images extracted from the complete data set. a) acquiring at least one preliminary image of the medium; b) defining an area of interest in the preliminary image; c) determining inter-transducer correlation matrices corresponding to the area of interest and to an unwanted area the unwanted area being the rest of the half-space in front of the probe; d) determining a characteristic matrix of the area of interest resulting from the product of the inverse of the inter-transducer correlation matrix of the unwanted area by the inter-transducer correlation matrix of the area of interest; e) calculating eigenvectors and eigenvalues of the characteristic matrix of the area of interest, these vectors, classified as a function of their corresponding eigenvalues, defining a transmission matrix; f) selecting the K eigenvectors associated with the K highest eigenvalues; g) firing K waves weighted by the selected K eigenvectors, each selected vector weighting the signals transmitted by the transducers (T1 to TN) during a firing, these vectors defining a truncated transmission matrix composed of, in a first part, the K vectors of the family of eigenvectors associated with the K highest eigenvalues of the characteristic matrix and, in a second part, columns of zeros corresponding to the firings that are not effected; h) receiving the signals returned by the medium; i) multiplying a reception matrix constituted of the acquired signals completed by data set to zero corresponding to the firings not effected by the inverse of the transmission matrix to obtain a complete data set; j) extracting low-resolution images from the complete data set as in synthetic aperture echographic imaging methods; and k) reconstructing the high-resolution image corresponding to the area of interest by coherent summing, as in synthetic aperture echographic imaging methods, of the low-resolution images extracted from the complete data set.