Do[aref[i] = -1.5 + HeavisideTheta[Sin[(i/8) + 1.4]], {i, imin + 1, imax - 1}]
Do[vref[i] = c Exp[aref[i]/2], {i, imin + 1, imax - 1}]
Do[atrue[i] = aref[i] + vec[i], {i, imin + 1, imax - 1}]
Do[vtrue[i] = c Exp[atrue[i]/2], {i, imin + 1, imax - 1}]