The increase of information in the medical environment caused by digital imaging settings is notable. The search and use of these technological tools aimed at medicine require a greater availability of storage, generating increasing costs. In medicine, together with information technology, there is a format of images used in exams, diagnostics, tomography, among others. This format, entitled DICOM, was created in order to standardize uses in medical devices for exam answers. An open question is the compression of DICOM data, in order to maintain quality, maintaining high rates of compression. This presents a new method for compressing and decompressing DICOM data using a dual cone bijector function and a video codec, called DC (Double Cone). This work offers 3 changes to the DC method (DC1, DC2 and DC3). The results obtained with a new technique show that the compression, although with loss, has a similarity index very close to the original image (SSIM = 0.99), and an accuracy ratio equal to 69.51, in the better case. The better performing version was the DC2.