A muffler-filter apparatus having a particulate trap using filter tubes with high temperature filter materials, like fiber in the form of yarn, woven yarn mat, or a non-woven, random array fiber mat, or various foams. Filter tubes have various structural configurations and are regenerated by axial propagation using ring heaters or stub rod heaters, by heating the entire length of the filter tube with a rod heater or some other full-length heater configuration. For regeneration, exhaust flow is bypassed using various valve configurations including a poppet valve, a shutter valve, or a tubular valve. Filter tube filters may also be self-regenerated by the heat from the exhaust gases as controlled by a throttle valve or on inclusion of fuel additives which lower particulate ignition temperature.