Xray DICOM Hist equalzation and noise removal

I have a 16-bit, dicom-formatted xray image. Because of the narrow range of the image histogram, I used CLACHE for histogram equalization.

However, the resultant image (attached below) after applying histogram equalization does have a noise as you can see in the attached image.

Can I get rid of this noise without losing information ? Could you please give an example code ?

I much appreciate your willingness to assist me with this matter.

fig, ax = plt.subplots(1, 1, figsize=(10, 10))
clahe = cv2.createCLAHE(clipLimit=150.0, tileGridSize=(8, 8))

dicom_xray_img = pydicom.dcmread(xrayPath)

src_img = dicom_xray_img.pixel_array
img_clahe = clahe.apply(src_img)

ax.imshow(img_clahe, cmap=plt.cm.bone)

The noise is there already in the original image - it is just amplified too… This being medical imaging, I would perhaps not do anything to it, it as noise removal might “alter the contents”, mask important small details and pose a risk in some situations.