Ten separate OLS drift and motion removal cycles failed a 0.000001 worst-case error limit in 431 fixed AOMIC designs

We tested repeated removal of drift and head motion in 431 fixed AOMIC working memory designs. Each cycle used unweighted ordinary least squares (OLS). It removed drift first and six centered motion terms second. The drift block had an intercept and cosine periods of at least 128 seconds. We compared repeated removal with one joint fit. Ten cycles failed the selected worst-case error limit of 0.000001 in all 431 designs. The error per unit input norm had median 0.7553 and range 0.0238 to 0.9760. The first sufficient count had median 469 and range 36 to 5414 cycles. We supply a reusable error and stopping audit tool. We also supply synthetic inputs that attain the bounds. The error formula comes from established alternating projection theory. Full regression matrices checked every main design. A fresh download gave the same results. The package preserves code, selected source data, hashes, a proof, and reproduction commands. These results apply to fixed nuisance designs. They do not measure brain activity or actual artifact amplitude.

ordinary least squares · fMRI · nuisance regression · alternating projections · motion correction · numerical error · AOMIC