Process for treating mineral materials, wherein: - crude mineral material is heated in a combustion unit (2, 3); - at least some of the flue gases generated by the combustion unit (2, 3) are recovered and sent to a first filtration device so as to recover particles in the flue gases; - particles of an agent that is reactive to at least one pollutant present in the flue gases are injected into the flue gases upstream of the first filtration device and loaded with pollutant such that the particles recovered in the first filtration device comprise a mixture of the particles of the pollutant-loaded reactive agent and dust, the size of the particles of the reactive agent being at least two times greater than the size of the dust, - the mixture of the dust and the particles of the pollutant-loaded reactive agent is sent to an aeraulic selection device so as to separate the dust from the particles of the loaded reactive agent; - the dust separated from the particles of the pollutant-loaded reactive agent is recovered at least in part in a second filtration device; - at least some of the particles of the reactive agent loaded with pollutant and separated from the dust by the aeraulic selection device are again injected into the flue gases, upstream of the first filtration device and downstream of the combustion unit (2, 3), so as to extend the contact time of the active agent with the pollutants, the active agent continuing to be loaded with pollutants before being extracted from the process, - wherein the process is a process for manufacturing cement, the combustion unit (2, 3) comprising at least one furnace for baking cement clinker and at least one preheater, the crude mineral material being successively preheated in the preheater and then baked in the furnace. - crude mineral material is heated in a combustion unit (2, 3); - at least some of the flue gases generated by the combustion unit (2, 3) are recovered and sent to a first filtration device so as to recover particles in the flue gases; - particles of an agent that is reactive to at least one pollutant present in the flue gases are injected into the flue gases upstream of the first filtration device and loaded with pollutant such that the particles recovered in the first filtration device comprise a mixture of the particles of the pollutant-loaded reactive agent and dust, the size of the particles of the reactive agent being at least two times greater than the size of the dust, - the mixture of the dust and the particles of the pollutant-loaded reactive agent is sent to an aeraulic selection device so as to separate the dust from the particles of the loaded reactive agent; - the dust separated from the particles of the pollutant-loaded reactive agent is recovered at least in part in a second filtration device; - at least some of the particles of the reactive agent loaded with pollutant and separated from the dust by the aeraulic selection device are again injected into the flue gases, upstream of the first filtration device and downstream of the combustion unit (2, 3), so as to extend the contact time of the active agent with the pollutants, the active agent continuing to be loaded with pollutants before being extracted from the process, - wherein the process is a process for manufacturing cement, the combustion unit (2, 3) comprising at least one furnace for baking cement clinker and at least one preheater, the crude mineral material being successively preheated in the preheater and then baked in the furnace.