An arrangement for imaging an object including a vessel, within which magnetic particles are present and which is placed in a region of action, comprising: - selection means for generating a magnetic selection field having a pattern in space of its magnetic field strength such that a first sub-zone having a low magnetic field strength and a second sub-zone having a higher magnetic field strength are formed in the region of action, - drive means for changing the position in space of the two sub-zones (301, 302) in the region of action by means of a magnetic drive field so that the magnetization of the magnetic material changes locally, - receiving means for acquiring detection signals, which detection signals depend on the magnetization in the region of action, which magnetization is influenced by the change in the position in space of the first and second sub-zone (301, 302), characterised by - processing means for reconstructing an image of the vessel based on a known concentration of the magnetic particles within the vessel and on vessel tree data about the progression of said vessel, said processing means comprising: a) transformation means for transforming the signal intensity of the acquired detection signals into an approximated image of a segment of interest of the vessel based on said vessel tree data, b) defining means for defining a volume, comprising volume elements, around said approximated image c) adapting means for stepwise and separately adapting the radii of said volume elements by integrating over the signal intensity of said volume elements, wherein the radii are adapted such that the integrated signal intensity over said volume elements equals the intensity expected from the known concentration of the magnetic particles in the vessel, d) reconstruction means for reconstructing an improved image by transforming the signal intensity of the acquired detection signals based on the adapted radii of said volume elements, e) iteration means for repeating the steps performed by the defining means, adapting means and reconstruction means until a predefined condition is fulfilled, wherein said improved image is used as approximated image in the step performed by the defining means, and f) displaying means for displaying said reconstructed image as volumes with the determined radii. - selection means for generating a magnetic selection field having a pattern in space of its magnetic field strength such that a first sub-zone having a low magnetic field strength and a second sub-zone having a higher magnetic field strength are formed in the region of action, - drive means for changing the position in space of the two sub-zones (301, 302) in the region of action by means of a magnetic drive field so that the magnetization of the magnetic material changes locally, - receiving means for acquiring detection signals, which detection signals depend on the magnetization in the region of action, which magnetization is influenced by the change in the position in space of the first and second sub-zone (301, 302), characterised by - processing means for reconstructing an image of the vessel based on a known concentration of the magnetic particles within the vessel and on vessel tree data about the progression of said vessel, a) transformation means for transforming the signal intensity of the acquired detection signals into an approximated image of a segment of interest of the vessel based on said vessel tree data, b) defining means for defining a volume, comprising volume elements, around said approximated image c) adapting means for stepwise and separately adapting the radii of said volume elements by integrating over the signal intensity of said volume elements, wherein the radii are adapted such that the integrated signal intensity over said volume elements equals the intensity expected from the known concentration of the magnetic particles in the vessel, d) reconstruction means for reconstructing an improved image by transforming the signal intensity of the acquired detection signals based on the adapted radii of said volume elements, e) iteration means for repeating the steps performed by the defining means, adapting means and reconstruction means until a predefined condition is fulfilled, wherein said improved image is used as approximated image in the step performed by the defining means, and f) displaying means for displaying said reconstructed image as volumes with the determined radii.