Pavement macrotexture is an important property that affects tire-pavement interactions like friction, tire pavement noise, splash and spray, and rolling resistance. Macrotexture measurement is generally divided into two classes: static measurements and dynamic measurements. Dynamic measurements are performed with vehicle mounted lasers that measure macrotexture at traffic speed. One drawback of these laser devices is the presence of "spikes" in the collected data which causes erroneous texture measurements. In this paper, we develop a data driven adaptive method that detects and removes the spikes from high speed laser texture measurements. The method is based on the discrete wavelet transform and can be summarized in the following three steps: (1) calculate the discrete wavelet transform of texture measurements, (2) detect and remove the "spikes" from the obtained wavelet coefficients, and (3) calculate the inverse discrete wavelet transform with the processed wavelet coefficients to obtain Mean Profile Depth (MPD) measurements with the "spikes" removed. The crucial step in the proposed method is step 2 which we detail in this paper. We compare the results of calculated MPD obtained by removing the "spikes" with the proposed method with the results obtained without removing the "spikes", and validate the proposed method with MPD measurements obtained with a Circular Texture Meter (CTMeter).