The quality of a digital or displayed image is influenced by many factors and is difficult to express in a single numerical metric.

Finding the maximum digital number DNmax and minimum digital number DNmin can be useful for statistical indicator Contrast ratio, contrast range. But these  may be inappropriate for some noisy images because one or two bad pixels could result in deceptively high contrast values. Standard deviation of contrast would be much less affected by outliers.

Another easily measured image property is modulation, M, defined as,

M = (DNmax - DNmin)/(DNmax+DNmin)

Because DNs are always positive, this definition insures that modulation is always between zero and one and unitless.

Another method to measure the quality of the image is Signal-to-Noise Ratio SNR which is the ratio of noise-free image contrast to the noise contrast.

Good luck

PSNR(peak signal to noise ratio), EME(Enhancement Measure) are some more parameters to decide the quality of image

you can consider ESSIM (edge-based structural similarity )if edges into image are very important. FSIM (feature-similarity) is another tool. Also the beta index (for edge-preservation estimation) and VIF (Variance inflation factor)  as an indicator of multicollinearity 

HSV error metrics like

SSIM, MSSIM, SNR,PSNR,IWSSIM, UQI, NQM, FSSIM, IWPSNR, IFC, WSNR, VSNR, CWSSIM, VIF, VIFP, 

mathematical error metrics such as

RMSE, MSE, RMAPE, RMSRE, NAE, RMAPE, RMARE

If you assume that background and foreground are two probabilistic distributions, you can use the Bhattacharyya distance between the two distributions, the higher the distance, the better the quality

The information content of ultrasound images appear at medium-to-large scale. Further, the information appears due to specular reflections from surfaces. Thus, the information is accessed via medium-scale directional derivative filters. The quality of the image depends on a lot of things, including what is being examined, but given a single scene, the best image has the highest contrast in mid-scale directional derivatives.

PSNR, Image Enhancement Factor, Contrast Enhancement Performance, Luminance Enhancement Performance, # of corners, Entropy, Structural Similarity Index Measure (SSIM), Energy etc. are the image quality measurement metrics.

In addition to all above recommendations given by experts, you should measure the SNR at your first step. It might help to see which correction or denoising you need to do. 

There are a full set of metrics available for comparing image quality as well as software that can be downloaded from our website http://www.medinfo.cs.ucy.ac.cy (or from Research gate). You may then extract quality and texture features between th original image and the processed.

Specifically look at the papers:

C.P. Loizou, C. Theofanous, M. Pantziaris, and T. Kasparis, “Despeckle filtering software toolbox for ultrasound imaging of the common carotid artery”, Computer Methods and Programs in Biomedicine, no. 114, pp. 109-124, January 2014.

C.P. Loizou, C.S. Pattichis, M. Pantzaris, T. Tyllis, and A.N. Nicolaides, "Quality Evaluation of Ultrasound Imaging in the Carotid Artery Based on Normalization and Speckle Reduction Filtering", Medical and Biological Engineering and Computing, vol. 44, issue 8, pp. 405-413, 2006