Image quality¶

sonosk.quality measures resolution and contrast on envelope data. All functions take envelope amplitudes. Values from a log-compressed image give wrong results.

Resolution¶

width(profile, x, level_db=-6) returns the width of the main lobe of an amplitude profile at level_db below its peak. The edges are found by linear interpolation between samples. A lateral profile through a point target gives the lateral resolution, and an axial profile gives the axial resolution.

from sonosk import quality

w6 = quality.width(profile, x)                  # -6 dB width
w20 = quality.width(profile, x, level_db=-20)   # -20 dB width

Contrast¶

For envelope samples \(s_i\) inside a region and \(s_o\) in the background:

\[ C = 20\log_{10}\frac{\bar{s}_i}{\bar{s}_o}, \qquad \mathrm{CNR} = \frac{|\bar{s}_i - \bar{s}_o|}{\sqrt{\sigma_i^2 + \sigma_o^2}} \]

quality.contrast_db(inside, background)
quality.cnr(inside, background)

Generalized CNR¶

The gCNR of Rodriguez-Molares et al. (2020) is one minus the overlap of the two sample distributions:

\[ \mathrm{gCNR} = 1 - \sum_k \min\left(h_i(k),\, h_o(k)\right) \]

where \(h_i\) and \(h_o\) are the normalised histograms on common bins. It lies between 0 (the regions cannot be told apart) and 1 (no overlap). In principle it does not change under a monotonic transform of the image, such as log compression, while the CNR does.

quality.gcnr(inside, background, bins=256)

Speckle¶

In fully developed speckle the envelope has a Rayleigh distribution and its mean over standard deviation is

\[ \mathrm{SNR}_s = \sqrt{\frac{\pi}{4 - \pi}} \approx 1.91 \]

(Burckhardt 1978). A simulated background region far from this value points to too few scatterers per resolution cell or to a coherent component.

quality.speckle_snr(background)
quality.RAYLEIGH_SNR          # 1.913

snr_db(signal, noise) is the ratio of RMS values in decibels.

References¶

Burckhardt C.B. Speckle in ultrasound B-mode scans. IEEE Trans. Sonics Ultrason. 25(1):1-6, 1978.

Rodriguez-Molares A. et al. The generalized contrast-to-noise ratio: a formal definition for lesion detectability. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 67(4):745-759, 2020.