diff --git a/.gitignore b/.gitignore
index 8875dc4..0fb5791 100644
--- a/.gitignore
+++ b/.gitignore
@@ -11,4 +11,4 @@ __pycache__/
 *.bak
 *.ahv
 *.hv
-*.v
\ No newline at end of file
+*.v
diff --git a/main_ISTA.py b/main_ISTA.py
index eeda971..17a577e 100644
--- a/main_ISTA.py
+++ b/main_ISTA.py
@@ -7,7 +7,7 @@
 """
 from cil.optimisation.algorithms import ISTA, Algorithm
 from cil.optimisation.functions import IndicatorBox, SGFunction
-from cil.optimisation.utilities import ConstantStepSize, Sampler, callbacks
+from cil.optimisation.utilities import ConstantStepSize, Preconditioner, Sampler, callbacks
 from petric import Dataset
 from sirf.contrib.partitioner import partitioner
 
@@ -28,14 +28,29 @@ def __call__(self, algorithm: Algorithm):
             raise StopIteration
 
 
+class MyPreconditioner(Preconditioner):
+    """
+    Example based on the row-sum of the Hessian of the log-likelihood. See: Tsai et al. Fast Quasi-Newton Algorithms
+    for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning,
+    IEEE TMI https://doi.org/10.1109/tmi.2017.2786865
+    """
+    def __init__(self, kappa):
+        # add an epsilon to avoid division by zero (probably should make epsilon dependent on kappa)
+        self.kappasq = kappa*kappa + 1e-6
+
+    def apply(self, algorithm, gradient, out=None):
+        return gradient.divide(self.kappasq, out=out)
+
+
 class Submission(ISTA):
+    """Stochastic subset version of preconditioned ISTA"""
+
     # note that `issubclass(ISTA, Algorithm) == True`
     def __init__(self, data: Dataset, num_subsets: int = 7, step_size: float = 1e-6,
                  update_objective_interval: int = 10):
         """
         Initialisation function, setting up data & (hyper)parameters.
         NB: in practice, `num_subsets` should likely be determined from the data.
-        WARNING: we also currently ignore the non-negativity constraint here.
         This is just an example. Try to modify and improve it!
         """
         data_sub, acq_models, obj_funs = partitioner.data_partition(data.acquired_data, data.additive_term,
@@ -45,11 +60,12 @@ def __init__(self, data: Dataset, num_subsets: int = 7, step_size: float = 1e-6,
             f.set_prior(data.prior)
 
         sampler = Sampler.random_without_replacement(len(obj_funs))
-        F = -SGFunction(obj_funs, sampler=sampler)      # negative to turn minimiser into maximiser
-        step_size_rule = ConstantStepSize(step_size)    # ISTA default step_size is 0.99*2.0/F.L
-        g = IndicatorBox(lower=1e-6, accelerated=False) # "non-negativity" constraint
+        f = -SGFunction(obj_funs, sampler=sampler)   # negative to turn minimiser into maximiser
+        step_size_rule = ConstantStepSize(step_size) # ISTA default step_size is 0.99*2.0/F.L
+        g = IndicatorBox(lower=0, accelerated=False) # non-negativity constraint
 
-        super().__init__(initial=data.OSEM_image, f=F, g=g, step_size=step_size_rule,
+        preconditioner = MyPreconditioner(data.kappa)
+        super().__init__(initial=data.OSEM_image, f=f, g=g, step_size=step_size_rule, preconditioner=preconditioner,
                          update_objective_interval=update_objective_interval)
 
 
diff --git a/petric.py b/petric.py
index 61e12f4..be560f0 100755
--- a/petric.py
+++ b/petric.py
@@ -143,7 +143,7 @@ def construct_RDP(penalty_strength, initial_image, kappa, max_scaling=1e-3):
     return prior
 
 
-Dataset = namedtuple('Dataset', ['acquired_data', 'additive_term', 'mult_factors', 'OSEM_image', 'prior'])
+Dataset = namedtuple('Dataset', ['acquired_data', 'additive_term', 'mult_factors', 'OSEM_image', 'prior', 'kappa'])
 
 
 def get_data(srcdir=".", outdir=OUTDIR, sirf_verbosity=0):
@@ -152,8 +152,7 @@ def get_data(srcdir=".", outdir=OUTDIR, sirf_verbosity=0):
     STIR.set_verbosity(sirf_verbosity)                # set to higher value to diagnose problems
     STIR.AcquisitionData.set_storage_scheme('memory') # needed for get_subsets()
 
-    _ = STIR.MessageRedirector(str(outdir / 'info.txt'), str(outdir / 'warnings.txt'),
-                               str(outdir / 'errors.txt'))
+    _ = STIR.MessageRedirector(str(outdir / 'info.txt'), str(outdir / 'warnings.txt'), str(outdir / 'errors.txt'))
     acquired_data = STIR.AcquisitionData(str(srcdir / 'prompts.hs'))
     additive_term = STIR.AcquisitionData(str(srcdir / 'additive_term.hs'))
     mult_factors = STIR.AcquisitionData(str(srcdir / 'mult_factors.hs'))
@@ -165,17 +164,16 @@ def get_data(srcdir=".", outdir=OUTDIR, sirf_verbosity=0):
         penalty_strength = 1 / 700 # default choice
     prior = construct_RDP(penalty_strength, OSEM_image, kappa)
 
-    return Dataset(acquired_data, additive_term, mult_factors, OSEM_image, prior)
+    return Dataset(acquired_data, additive_term, mult_factors, OSEM_image, prior, kappa)
 
 
 if SRCDIR.is_dir():
-    data_dirs_metrics = [
-        (SRCDIR / "Siemens_mMR_NEMA_IQ", OUTDIR / "mMR_NEMA",
-         [MetricsWithTimeout(outdir=OUTDIR / "mMR_NEMA", transverse_slice=72, coronal_slice=109)]),
-        (SRCDIR / "NeuroLF_Hoffman_Dataset", OUTDIR / "NeuroLF_Hoffman",
-         [MetricsWithTimeout(outdir=OUTDIR / "NeuroLF_Hoffman", transverse_slice=72)]),
-        (SRCDIR / "Siemens_Vision600_thorax", OUTDIR / "Vision600_thorax",
-         [MetricsWithTimeout(outdir=OUTDIR / "Vision600_thorax")])]
+    data_dirs_metrics = [(SRCDIR / "Siemens_mMR_NEMA_IQ", OUTDIR / "mMR_NEMA",
+                          [MetricsWithTimeout(outdir=OUTDIR / "mMR_NEMA", transverse_slice=72, coronal_slice=109)]),
+                         (SRCDIR / "NeuroLF_Hoffman_Dataset", OUTDIR / "NeuroLF_Hoffman",
+                          [MetricsWithTimeout(outdir=OUTDIR / "NeuroLF_Hoffman", transverse_slice=72)]),
+                         (SRCDIR / "Siemens_Vision600_thorax", OUTDIR / "Vision600_thorax",
+                          [MetricsWithTimeout(outdir=OUTDIR / "Vision600_thorax")])]
 else:
     log.warning("Source directory does not exist: %s", SRCDIR)
     data_dirs_metrics = [(None, None, [])]