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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def log_transform(image):
    '''Renormalize image intensities to log space
    
    Returns a tuple of transformed image and a dictionary to be passed into
    inverse_log_transform. The minimum and maximum from the dictionary
    can be applied to an image by the inverse_log_transform to 
    convert it back to its former intensity values.
    '''
    orig_min, orig_max = scipy.ndimage.extrema(image)[:2]
    #
    # We add 1/2 bit noise to an 8 bit image to give the log a bottom
    #
    limage = image.copy()
    noise_min = orig_min + (orig_max-orig_min)/256.0+np.finfo(image.dtype).eps
    limage[limage < noise_min] = noise_min
    d = { "noise_min":noise_min}
    limage = np.log(limage)
    log_min, log_max = scipy.ndimage.extrema(limage)[:2]
    d["log_min"] = log_min
    d["log_max"] = log_max
    return stretch(limage), d