Short-lag spatial coherence (SLSC) imaging displays the spatial coherence between backscattered ultrasound echoes instead of their signal amplitudes and is more robust to noise and clutter artifacts when compared with traditional delay-and-sum (DAS) B-mode imaging. However, SLSC imaging does not consider the content of images formed with different lags, and thus does not exploit the differences in tissue texture at each short-lag value. Our proposed method improves SLSC imaging by weighting the addition of lag values (i.e., M-weighting) and by applying robust principal component analysis (RPCA) to search for a low-dimensional subspace for projecting coherence images created with different lag values. The RPCA-based projections are considered to be denoised versions of the originals that are then weighted and added across lags to yield a final robust SLSC (R-SLSC) image. Our approach was tested on simulation, phantom, and in vivo liver data. Relative to DAS B-mode images, the mean contrast, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) improvements with R-SLSC images are 21.22 dB, 2.54, and 2.36, respectively, when averaged over simulated, phantom, and in vivo data and over all lags considered, which corresponds to mean improvements of 96.4%, 121.2%, and 120.5%, respectively. When compared with SLSC images, the corresponding mean improvements with R-SLSC images were 7.38 dB, 1.52, and 1.30, respectively (i.e., mean improvements of 14.5%, 50.5%, and 43.2%, respectively). Results show great promise for smoothing out the tissue texture of SLSC images and enhancing anechoic or hypoechoic target visibility at higher lag values, which could be useful in clinical tasks such as breast cyst visualization, liver vessel tracking, and obese patient imaging.