diff --git a/proximal/lin_ops/conv.py b/proximal/lin_ops/conv.py
index 433d3d6..eab5c9c 100644
--- a/proximal/lin_ops/conv.py
+++ b/proximal/lin_ops/conv.py
@@ -29,15 +29,21 @@ def init_kernel(self):
                 self.kernel = np.stack((self.kernel,) * arg.shape[2], axis=-1)
 
             # Halide kernel
-            if self.implementation == Impl['halide'] and \
-               (len(arg.shape) == 2 or (len(arg.shape) == 3 and arg.dims == 2)):
+            if self.implementation == Impl["halide"] and (
+                len(arg.shape) == 2 or (len(arg.shape) == 3 and arg.dims == 2)
+            ):
                 self.kernel = np.asfortranarray(self.kernel.astype(np.float32))
-                # Halide FFT (pack into diag)
-                # TODO: FIX IMREAL LATER
+
+                # Fourier-transformed real-valued signal has Hermitian symmetry.
+                # Only the right-half plane is needed by Halide-generated
+                # algorithms as the input.
+                #
+                # TODO: Move this logic to proximal.utils
                 hsize = arg.shape if len(arg.shape) == 3 else arg.shape + (1,)
                 output_fft_tmp = np.zeros((int((hsize[0] + 1) / 2) + 1, hsize[1], hsize[2]),
                                           dtype=np.complex64, order='F')
 
+                # Halide FFT (pack into diag)
                 Halide('fft2_r2c', target_shape=hsize[:2]).fft2_r2c(self.kernel, self.kernel.shape[1] // 2,
                                                 self.kernel.shape[0] // 2, output_fft_tmp)
                 self.forward_kernel[:] = 0.
@@ -56,8 +62,9 @@ def forward(self, inputs, outputs):
         Reads from inputs and writes to outputs.
         """
         self.init_kernel()
-        if self.implementation == Impl['halide'] and \
-                (len(self.shape) == 2 or (len(self.shape) == 3 and self.dims == 2)):
+        if self.implementation == Impl["halide"] and (
+            len(self.shape) == 2 or (len(self.shape) == 3 and self.dims == 2)
+        ):
 
             # Halide implementation
             Halide('A_conv').A_conv(inputs[0], self.kernel, self.tmpout)  # Call
diff --git a/proximal/prox_fns/sum_squares.py b/proximal/prox_fns/sum_squares.py
index 7924a4d..dec9869 100644
--- a/proximal/prox_fns/sum_squares.py
+++ b/proximal/prox_fns/sum_squares.py
@@ -115,10 +115,16 @@ def __init__(self,
 
             self.freq_shape = self.K.orig_end.variables()[0].shape
             self.freq_diag = np.reshape(self.freq_diag, self.freq_shape)
-            if implem == Impl['halide'] and \
-                    (len(self.freq_shape) == 2 or (len(self.freq_shape) == 2 and
-                                                   self.freq_dims == 2)):
-                # TODO: FIX REAL TO IMAG
+            if implem == Impl["halide"] and (
+                len(self.freq_shape) == 2
+                or (len(self.freq_shape) == 3 and self.freq_dims == 2)
+            ):
+
+                # Fourier-transformed real-valued signal has Hermitian symmetry.
+                # Only the right-half plane is needed by Halide-generated
+                # algorithms as the input.
+                #
+                # TODO: Move this logic to proximal.utils
                 hsize = self.freq_shape if len(
                     self.freq_shape) == 3 else (self.freq_shape[0],
                                                 self.freq_shape[1], 1)
@@ -212,9 +218,10 @@ def solve(self, b: memoized_expr, rho=None, v=None, lin_solver="lsqr", hash=None
         # KtK operator is diagonal in frequency domain.
         elif self.freq_diag is not None:
             # Frequency inversion
-            if self.implementation == Impl['halide'] and \
-                    (len(self.freq_shape) == 2 or
-                     (len(self.freq_shape) == 2 and self.freq_dims == 2)):
+            if self.implementation == Impl["halide"] and (
+                len(self.freq_shape) == 2
+                or (len(self.freq_shape) == 3 and self.freq_dims == 2)
+            ):
 
                 ftmp_halide_out = np.empty(self.freq_shape, dtype=np.float32, order='F')